Digital SAT Mock Test - 5 - SAT MCQ

Choice 2 is the best answer because it most effectively states the main idea of the text, which is that Heidi is delighted and fascinated by an image she sees in one of Grandmama’s books. In the text, Heidi screams upon first seeing the picture of the green pasture. In another context, such a reaction might suggest fear, but here the reaction is followed by descriptions of an image that’s peaceful rather than scary. The text goes on to describe Heidi’s eyes as “glowing” and states that she “devoured the scene,” suggesting that the image delights and fascinates her so much that she wants to examine every detail. Together, these descriptions suggest that Heidi is thrilled and intrigued by the image in the book.
Choice 1 is incorrect because there’s nothing in the text to suggest that Heidi is upset before seeing the peaceful image of the green pasture. Before Heidi sees that image, the text describes her as “looking with wondering eyes at the splendid pictures” in the book, suggesting that Heidi is intrigued, not that she’s unhappy.
Choice 3 is incorrect. Although Heidi screams upon first seeing the image, the text’s description of the image and Heidi’s other reactions to it suggest that she is screaming with delight, not fear. The text describes the images in the book as “splendid” and the particular image that causes her to scream as peaceful rather than frightening. It also describes Heidi’s eyes as “glowing” and states that she “devoured the scene,” suggesting that the image of the green pasture delights and fascinates her so much that she wants to examine every detail.
Choice 4 is incorrect because it’s unclear from the text whether Heidi has ever seen a shepherd with his sheep before. The text merely suggests that she is delighted and fascinated by the image of the shepherd and his sheep.

Choice 2 is the best answer because it presents a finding that, if true, would most directly support the arts journalist’s claim about Enwezor’s work as a curator and art historian. In the text, the arts journalist asserts that Enwezor wished not just to focus on modern African artists but also to show “how their work fits into the larger context of global modern art and art history,” or how their work relates to artistic developments and work by other artists elsewhere in the world. The description of Postwar: Art Between the Pacific and the Atlantic, 1945–1965 indicates that Enwezor and Siegel’s exhibition brought works by African artists together with works by artists from other countries, thus supporting the arts journalist’s claim that Enwezor sought to show works by African artists in a context of global modern art and art history.
Choice 1 is incorrect because it describes a retrospective that wouldn’t support the arts journalist’s claim that Enwezor wanted to show how works by modern African artists fit into the larger context of global modern art and art history. The description of El Anatsui: Triumphant Scale indicates that the retrospective focused only on the work of a single African artist, El Anatsui. The description doesn’t suggest that the exhibition showed how El Anatsui’s works fit into a global artistic context.
Choice 3 is incorrect because it describes an exhibition that wouldn’t support the arts journalist’s claim that Enwezor wanted to show how works by modern African artists relate to the larger context of global modern art and art history. The description of The Short Century: Independence and Liberation Movements in Africa, 1945–1994 indicates that the exhibition showed how African artists were influenced by movements for independence from European colonial powers following the Second World War. Although this suggests that Enwezor intended the exhibition to place works by African artists in a political context, it doesn’t indicate that the works were placed in a global artistic context.
Choice 4 is incorrect because it describes an exhibition that wouldn’t support the arts journalist’s claim that Enwezor wanted to show how works by modern African artists relate to the larger context of global modern art and art history. The description of African Photographers, 1940 to the Present indicates that the exhibition was intended to reveal the broad range of approaches taken by African photographers, not that the exhibition showed how photography by African artists fits into a global artistic context.

Choice 2 is the best answer. The lighter bars show what happened when the announcement was to come before the election, and the darker bars show what happened when the announcement was to come after the election. For all three of the outcomes, the light and dark bars are virtually the same, demonstrating that the announcement timing didn’t actually make a difference.
Choice 1 is incorrect. This accurately describes some data from the graph, but it doesn’t weaken the hypothesis. It doesn’t include the “announcement after election” data for comparison.
Choice 3 is incorrect. This accurately describes some data from the graph, but it doesn’t weaken the hypothesis. It doesn’t include the “announcement after election” data for comparison.
Choice 4 is incorrect. This accurately describes some data from the graph, but it doesn’t weaken the hypothesis. It doesn’t include the “announcement before election” data for comparison.

Choice 1 is the best answer because it presents the quotation that most directly illustrates the claim that Whitman’s poem suggests that its readers haven’t fully understood themselves. This quotation makes that point directly by saying to readers, “You have not known what you are.” The quotation goes on to reinforce this point using a metaphor of sleep, saying that readers have “slumber’d” and that their “eyelids have been the same as closed most of the time.”

Choice 2 is incorrect because this quotation doesn’t suggest that readers haven’t fully understood themselves but instead characterizes readers as “immense” and “interminable.” Although immense and interminable things can be difficult to understand, this quotation doesn’t make that point.

Choice 3 is incorrect because this quotation doesn’t suggest that readers haven’t fully understood themselves but instead conveys the speaker’s regret over not having celebrated readers sooner. In fact, this quotation says nothing at all about readers themselves—it’s focused solely on the speaker’s feelings about readers.

Choice 4 is incorrect because this quotation doesn’t suggest that readers haven’t fully understood themselves; instead, this quotation makes the point that the speaker has understood readers and is determined to create “hymns” about them.

Choice 2 is the best answer. The text states that archaeologists are interested in using scents to better understand "ancient rituals, trade, social hierarchies, and medicine," all of which are important aspects of ancient life.

Choice 1 is incorrect. The text doesn’t say anything about investigating if people’s sense of smell has declined in recent centuries. It says that scents fade over time—not that people have gotten worse at smelling scents. Choice 3 is incorrect. The text says that archaeologists are interested in using scents to better understand "ancient rituals, trade, social hierarchies, and medicine," but it doesn’t say anything about ancient scents being enjoyable to people today.
Choice 4 is incorrect. The text doesn’t say anything about developing new medicines. Rather, it says that archaeologists are interested in using scents to better understand "ancient rituals, trade, social hierarchies, and medicine."

Choice 1 is the best answer. In one example, musicians made less money than expected by using the “pay as you wish” model. In the other example, a musician made more money than expected. This suggests that some musicians may have more success than others using the “pay as you wish” model.
Choice 2 is incorrect. This inference isn’t supported. In the examples provided, the individual musician was more successful with the “pay as you wish” model than the band was.
Choice 3 is incorrect. This inference isn’t supported. The passage provides no instances in which musicians changed the suggested prices of their songs or albums, nor does it mention this as a possibility.
Choice 4 is incorrect. This inference isn’t supported. The text never discusses the differences in popularity of different musicians, so there is no basis to make this inference.

Choice 2 is the best answer. By showing that "any difference" in taste was quickly overcome by "the force of [Marianne’s] arguments," this choice effectively demonstrates Marianne’s "ability to persuade others."

Choice 1 is incorrect. This choice doesn’t effectively illustrate the claim. This choice shows that Marianne and John share an interest in music and dancing, but it doesn’t provide evidence of Marianne’s "ability to persuade others."

Choice 3 is incorrect. This choice doesn’t effectively illustrate the claim. This choice shows that Marianne enjoys talking about her interests, but it doesn’t provide evidence of Marianne’s "ability to persuade others.

Choice 4 is incorrect. This choice doesn’t effectively illustrate the claim. This choice shows that Marianne and John share many interests and generally agree on music and dancing, but it doesn’t provide evidence of Marianne’s "ability to persuade others."

Choice 3 is the best answer. The text describes the comfort rating scale: from −3 (very cold) to +3 (very hot), with 0 being neutral. Participant 20 gave a −2 comfort rating, a full three points colder on the scale than the other two participants.

Choice 1 is incorrect. This choice misreads the table. Participant 1 and participant 21 reported the same level of comfort, but participant 20’s comfort level was three points lower.
Choice 2 is incorrect. This choice doesn’t use data from the table. The table only shows us one survey, so we don’t know if the participants’ ratings varied throughout the day.
Choice 4 is incorrect. This choice misreads the table. Participant 1 and participant 21 reported the same level of comfort.

Choice 1 is the best answer because it most accurately states the main idea of the text. According to the text, Eugene Wigner hypothesized that a crystal could exist that would be composed of electrons and have a honeycomb-like shape. The text goes on to say that the existence of the Wigner crystal remained unconfirmed until Feng Wang and colleagues were able to make an impression of one using two semiconductors and an ultrathin sheet of graphene. Thus, the main idea is that researchers have obtained the most definitive evidence to date of the existence of the Wigner crystal.

Choice 2 is incorrect because the text focuses on one kind of crystal—the Wigner crystal— and doesn’t discuss crystalline structures in general. And although the text conveys that Wang and colleagues figured out a way to capture an image of a Wigner crystal, it doesn’t address the idea of applying this approach to other types of crystals.
Choice 3 is incorrect because the text describes in general the process Wang and colleagues followed to obtain an impression of the Wigner crystal; it doesn’t address the relative importance of each component in that process.
Choice 4 is incorrect because the text doesn’t state that researchers had a hard time getting an impression of the Wigner crystal because of its honeycomb structure. Nothing in the text indicates why it took so long to prove the existence of this crystal or take an impression of it.

Choice 1 is the best answer because it presents the quotation that most directly illustrates the claim that Whitman’s poem suggests that its readers haven’t fully understood themselves. This quotation makes that point directly by saying to readers, “You have not known what you are.” The quotation goes on to reinforce this point using a metaphor of sleep, saying that readers have “slumber’d” and that their “eyelids have been the same as closed most of the time.”

Choice 2 is incorrect because this quotation doesn’t suggest that readers haven’t fully understood themselves but instead characterizes readers as “immense” and “interminable.” Although immense and interminable things can be difficult to understand, this quotation doesn’t make that point.

Choice 3 is incorrect because this quotation doesn’t suggest that readers haven’t fully understood themselves but instead conveys the speaker’s regret over not having celebrated readers sooner. In fact, this quotation says nothing at all about readers themselves—it’s focused solely on the speaker’s feelings about readers.

Choice 4 is incorrect because this quotation doesn’t suggest that readers haven’t fully understood themselves; instead, this quotation makes the point that the speaker has understood readers and is determined to create “hymns” about them.

• Choice A is the best answer because it presents data from the table that most effectively complete the statement about the rates at which employment shifted in France and the United States. The text states that over the last two hundred years employment in the agricultural sector has declined while employment in the service sector has risen in both France and the US, and the data from the table reflect these trends. The text asserts, however, that the transition from agriculture to services “happened at very different rates in the two countries.” This assertion is best supported by a comparison of data from 1900 and 1950: the table shows that in those years, employment in agriculture went from 43% to 32% in France (a decline of 11 percentage points) and from 41% to 14% in the US (a decline of 27 percentage points), and that employment in services went from 28% to 35% in France (an increase of 7 percentage points) and from 31% to 53% in the US (an increase of 22 percentage points). In other words, the rate of change was greater in the US than in France for both sectors.
• Choice B is incorrect because comparing the data for 1800 and 2012 would suggest a similar rate of change in the two countries, not very different rates: employment in agriculture went from 64% in 1800 to 3% in 2012 in France, which is close to the change from 68% in 1800 to 2% in 2012 in the US, while employment in services went from 14% in 1800 to 76% in 2012 in France, which is close to the change from 13% in 1800 to 80% in 2012 in the US.
• Choice C is incorrect because comparing the data for 1900 and 2012 would suggest a similar rate of change in the two countries rather than very different rates: employment in agriculture went from 43% in 1900 to 3% in 2012 in France, which is close to the change from 41% in 1900 to 2% in 2012 in the US, while employment in services went from 28% in 1900 to 76% in 2012 in France, which is close to the change from 31% in 1900 to 80% in 2012 in the US.
• Choice D is incorrect because comparing the data for 1800 and 1900 would suggest a similar rate of change in the two countries, not very different rates: employment in agriculture went from 64% in 1800 to 43% in 1900 in France, which is fairly close to the change from 68% in 1800 to 41% in 1900 in the US, while employment in services went from 14% in 1800 to 28% in 1900 in France, which is close to the change from 13% in 1800 to 31% in 1900 in the US.

• Choice D is the best answer because it provides the most direct support from the table for the claim that the plants growing in close proximity to other plants gained an advantage at an early developmental stage. The table shows the total number of juvenile plants from five species that were found growing on bare ground and in patches of vegetation as well as the percentage of the total number of each species that were growing in patches of vegetation. For each of the five species, more than 50% of the juvenile plants were growing in patches of vegetation. The text notes, however, that a random distribution of plants across the landscape should result in only about 15% of the plants being found in patches of vegetation. In other words, for each of the five species, the percentage of juvenile plants found growing in patches of vegetation was substantially higher than could be explained by chance alone. This finding supports the claim in the text: if plants growing in patches are overrepresented among plants that have survived to the juvenile stage, as the data show they are, then it suggests that it’s advantageous for plants at an early stage of development to grow in patches of vegetation.
• Choice A is incorrect because the statement that less than 75% of juvenile plants were found growing in patches of vegetation, while true, doesn’t clearly support the claim that the plants growing in close proximity to other plants gained an advantage at an early developmental stage. Saying that less than 75% of plants were found in patches doesn’t indicate how the percentage growing in patches compares with the percentage that would be expected to grow in patches on the basis of chance alone, which is the information necessary to evaluate whether the claim in the text has support in the table. Put another way, if the percentage of plants found growing in patches was 15% or less, it would be true that less than 75% were found in patches, but the data would in fact weaken the claim in the text, not strengthen it, since the data would show that growing in patches wasn’t advantageous.
• Choice B is incorrect because only 12 plants of this species were found growing in patches, which was the lowest number of any species, not the greatest number. Additionally, even if it were true that this species had the greatest number of plants growing in patches, the finding would be irrelevant to the claim that plants of all five species gained an advantage by growing in close proximity to other plants.
• Choice C is incorrect because 59.1% of the plants of these species were found growing in patches, which is a far greater percentage, not a lower percentage, than what would be expected if plants were randomly distributed (around 15%). Additionally, if it were true that the percentage of plants growing in patches was lower for these species than what would be expected from chance alone, that finding would weaken, not strengthen, the claim that growing in patches is advantageous.

• Choice D is the best answer. “As a result” logically signals that the claim in this sentence—that spiders can cling to and climb almost any surface—is because of the previous information about the bonding properties of spiders’ spatulae.
• Choice A is incorrect because “for instance” illogically signals that the claim in this sentence exemplifies the information in the previous sentences. Instead, the claim is because of the previous information about the bonding properties of spiders’ spatulae.
• Choice B is incorrect because “however” illogically signals that the claim in this sentence contrasts with the information in the previous sentences. Instead, the claim is because of the previous information about the bonding properties of spiders’ spatulae.
• Choice C is incorrect because “similarly” illogically signals that the claim in this sentence is similar to, but separate from, the information in the previous sentences. Instead, the claim is because of the previous information about the bonding properties of spiders’ spatulae.

• Choice B is the best answer because it most logically completes the text’s discussion of the art installation Anthem. In this context, “inventive” means characterized by invention and creativity. The text explains that critics’ responses to the installation involved praise for Tsang’s creative transformation of a space into a dynamic exhibit with huge images and lots of sound. This context conveys that the critics found the piece particularly creative.
• Choice A is incorrect because the text indicates that critics praised the installation for being dynamic and including huge images and lots of sound, and it wouldn’t make sense to describe such an exhibit as “restrained,” or limited and not extravagant or showy.
• Choice C is incorrect because it wouldn’t make sense to say that critics found the installation “inexplicable,” or incapable of being explained or interpreted, since the critics were able to explain their praise for the installation’s transformation of a space with huge images and lots of sound.
• Choice D is incorrect because the text focuses on the idea that critics praised Tsang for creatively transforming a space into a dynamic exhibit, not that they found the installation “mystifying,” or bewildering and hard to understand. Nothing in the text suggests that the critics couldn’t understand the piece.

• Choice D is the best answer because it presents a finding that, if true, would most directly support the researchers’ hypothesis about the connection between the dusky shark population decline and the eastern oyster population decline. The text indicates that although dusky sharks don’t usually eat eastern oysters, they do consume cownose rays, which are the main predators of eastern oysters. An increase in the abundance of cownose rays in the region in response to a decline in the abundance of dusky sharks would directly support the researchers’ hypothesis: a higher number of cownose rays would consume more eastern oysters, driving down the oyster population.
• Choice A is incorrect because a finding that there’s an association between a decline in the regional abundance of some of dusky sharks’ prey and the regional abundance of dusky sharks wouldn’t directly support the researchers’ hypothesis that a decline in dusky sharks has led to a decline in eastern oysters in the region. Although such a finding might help explain why shark abundance has declined, it would reveal nothing about whether the shark decline is related to the oyster decline.
• Choice B is incorrect because a finding that eastern oyster abundance tends to be greater when dusky sharks and cownose rays are present than when only dusky sharks are present wouldn’t support the researchers’ hypothesis that a decline in dusky sharks has led to a decline in eastern oysters in the region. The text indicates that the sharks prey on the rays, which are the main predators of the oysters; if oyster abundance is found to be greater when rays are present than when rays are absent, that would suggest that rays aren’t keeping oyster abundance down, and thus that a decline in rays’ predators, which would be expected to lead to an increase in the abundance of rays, wouldn’t bring about a decline in oyster abundance as the researchers hypothesize.
• Choice C is incorrect because a finding that consumption of eastern oysters by cownose rays increased substantially before dusky sharks declined in regional abundance wouldn’t support the researchers’ hypothesis that the decline in dusky sharks has led to a decline in eastern oysters in the region. Such a finding would suggest that some factor other than shark abundance led to an increase in rays’ consumption of oysters and thus to a decrease in oyster abundance, thereby weakening the researchers’ hypothesis.

• Choice C is the best answer. The convention being tested is punctuation between a subordinate clause and a main clause. This choice correctly uses a comma to mark the boundary between the subordinate clause (“While…lifelike”) and the main clause (“others look to the past”).
• Choice A is incorrect because it results in an incomplete sentence with no main clause.
• Choice B is incorrect because it fails to mark the boundary between the subordinate clause (“While…lifelike”) and the main clause (“others…past”).
• Choice D is incorrect because it results in an incomplete sentence with no main clause.

• Choice D is the best answer. The convention being tested is punctuation between a verb and a preposition. When, as in this case, a verb (“is added”) is immediately followed by a preposition (“whenever”), no punctuation is needed.
• Choice A is incorrect because no punctuation is needed between the verb and the preposition.
• Choice B is incorrect because no punctuation is needed between the verb and the preposition.
• Choice C is incorrect because no punctuation is needed between the verb and the preposition.

Choice B is the correct answer. Let x and y be the number of easy and hard puzzles, respectively, that Tina solved. Since she solved a total of 50 puzzles, it follows that x + y = 50. She earned a total of 1,950 points, so it must also be true that 30x + 60y = 1,950. Dividing both sides of this equation by 30 gives x + 2y = 65. Subtracting the first equation, x + y = 50, from the second equation, x + 2y = 65, gives y = 15. Therefore, Tina solved 15 hard puzzles.
Alternatively: Let x be the number of easy puzzles Tina solved. Then, 50 - x is the number of hard puzzles she solved. And since she earned a total of 1,950 points, it must be true that 30x + 60(50 - x) = 1,950. Solving this equation for x gives x = 35, and so 50 - x = 15. Therefore, Tina solved 15 hard puzzles.
Choices A and C are incorrect because if the number of hard puzzles Tina solved were as they indicate, the total number of points she would earn will not be 1,950. The incorrect answer in choice D could be the result of interchanging the number of hard puzzles and easy puzzles.

Choice D is correct. Since f(x – 1) = 2x + 3 for all values of x, f(−3) = f(−2 – 1) = 2(−2) + 3, and so the value of f(−3) is −1.  Alternatively: 2x + 3 can be rewritten as 2(x – 1) + 5, and since f(x – 1) = 2(x – 1) + 5 for all values of x, it follows that f(x) = 2x + 5 for all values of x. Substituting −3 for x in this equation gives  f(−3) = 2(−3) + 5 = –1.
Choices A, B, and C are incorrect because f is a function, and there is one and only one value for f(−3), which as shown above is −1. Therefore, neither of the choices, −7, −5, or −3 can be the value of f(−3).

Choice B is the correct answer. In 2012, the total population of individuals in the United States who were between 14 and 17 years old (inclusive) was about 17 million, which is 105 times the size of the survey sample, 170. Since of those surveyed, 39 teenagers aged 16 to 17 had a summer job, it follows that the best estimate of the total number of individuals aged 16 to 17 in the United States who had a summer job in 2012 was 39 × 10⁵ = 3,900,000.
Choices A, C, and D are incorrect and are likely the result of either conceptual or calculation errors made. 

Choice B is correct. Looking at the graph, it can be concluded that there is an increase of fewer than 10 students during quarters 4 through 6, quarters 11 through 14, and quarters 13 through 16. There is an increase of more than 20 students during quarters 7 through 10. Therefore, of the four ranges given in the answer choices, the greatest increase in the number of students occurs during quarters 7 through 10.
Choices A, C, and D are incorrect. There is an increase of fewer than 10 students during quarters 4 through 6, quarters 11 through 14, and quarters 13 through 16. There is an increase of more than 20 students during quarters 7 through 10. Therefore, the greatest increase in the number of students does not occur in the ranges given in choices A, C, and D.

Choice A is correct. According to the scatterplot, the player with 450 times at bat had approximately 113 hits (the y-coordinate of the point representing this player is approximately halfway between 100 and 125). The line of best fit predicts approximately 123 hits. Therefore, the actual number of hits made by this player is approximately 10 fewer than the number of hits predicted by the line of best fit.
Choices B, C, and D are incorrect because each gives a value much greater than 10, which is the best approximation of how many fewer hits were made by the player with 450 times at bat than predicted by the line of best fit. 

Choice B is correct. Since the 327 9th-grade students are a random sample selected from all 9th-grade students in the school, the sample can be considered to be representative of all the 9th-grade students in the school. This means that the proportion of 9th-grade students in the school who had a GPA of 3.0 or greater can be estimated using the proportion of 9th-grade students who had a GPA of 3.0 or greater in the sample. Of the 327 9th-grade students in the study, 61 + 95 = 156 students had a GPA of 3.0 or greater. Therefore, the probability that a 9th-grade student at the school chosen at random had a GPA of 3.0 or greater is estimated to be 157/327 ≈ 0.477, which rounds to 0.48.
Choice A is incorrect. This answer choice is the result of dividing the number of students in the study enrolled in Propel with a GPA of 3.0 or greater, 61, by the number of students in the study not enrolled in Propel with a GPA of 3.0 or greater, 95, rather than dividing the total number of students with a GPA of 3.0 or higher by the total number of students in the study. Choice C is incorrect. This answer choice reflects the probability that a 9th-grade student, selected at random, is enrolled in Propel. It is the result of dividing the total number of students enrolled in Propel, rather than the total number of students with a GPA of 3.0 or greater, by the total number of students in the study. Choice D is incorrect. This answer choice reflects the probability that a 9th-grade student, selected at random, is enrolled in Propel and has a GPA of 3.0 or greater. It is the result of dividing the number of students who both are enrolled in Propel and had a GPA of 3.0 or greater, rather than all students who had a GPA of 3.0 or greater, by the total number of students in the study. 

If points A and B are on the circle:

In this case, we are looking for the length of  so let's call that x. We know that the measure of the interior angle is 120°, and that the circumference of the circle is 30:

Cross multiply: 360x = 3600
Divide both sides by 360: x = 10

Original formula: 
Divide both sides by l: 
Multiply both sides by 3: 

One way to analyze a formula is by “dimensional analysis.” This is simply a way to check that the units in the formula represent what they are supposed to represent. For instance, we are told that the expression 240 + 3nt represents the cost, in dollars, of the project. This means that both terms in this expression must be in dollars. Notice, also, that n is the number of servers and t is the number of hours. Let's use a ? to represent the units of the number 3 in the expression 3nt. Translating the term into units, this gives us 
(?)(servers)(hours) = $
Divide by (servers)(hours): ? =

In other words, it costs the company 3 dollars per hour per server.

Substitute 
(Law #3 from Chapter 9, Lesson 9): 
Cross-multiply: x² = 16
Take the square root: x = ±4
Recall the other equation: 
Law #6 from Chapter 9, Lesson 9: x^b-a = 16
Substitute x = ±4: (±4)^b-a = 16
Notice that both 4² = 16 and (-4)² = 16,
therefore: b - a = 2

The standard deviation of a set of numbers tells us how “spread out” the data are from the average—the greater the standard deviation, the greater the spread from the average. It should be clear by inspection that the scores for Class B are more “clustered” than the scores for Class A. For instance, there is only a 5-point difference between the lowest and highest scores in Class B, but a 31-point difference between the lowest and highest scores in Class A. This means that the standard deviation of the scores in Class B is smaller.

Using the Factor Theorem, we know that if a quadratic has zeroes at x = 1 and x = 5, it must have factors of (x - 1) and (x - 5). Since a quadratic can only have two linear factors, fmust be of the form f(x) = k(x - 1)(x - 5).
Substitute x = 3 and y = -2 for the f(x) = k(x - 1)(x - 5).
Substitute x = 3 and y = -2 for the coordinates of vertex: -2 = k(3 - 1)(3 - 5)
Simplify: -2 = k(2)(-2)
Simplify: -2 = -4k
Divide by -4: 1/2 = k
Therefore the equation of the function is  and we can find its y-intercept by substituting x = 0: 
Simplify: f(0) = 5/2 or 2.5

To find the equation of the line of best fit, we can take two points on the line and then use the point-slope formula to find the equation of the line. To get the most accurate representation of the line, we should choose two points that are fairly far apart, but whose coordinates are easy to determine. The graph shows that this line appears to pass through the points (60, 3) and (100, 9), and so, by the slope formula we can calculate that the slope is (9 - 3)/ (100 - 60) = 6/40 = 3/20. Using the first point in the point-slope formula gives 
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