CAT Exam > CAT Questions > DIRECTIONSfor the question:Solve the followin...
Start Learning for Free
DIRECTIONS for the question: Solve the following question and mark the best possible option.
A quadratic function f(x) attains a maximum of 10 at x = 2. The value of the function at x = 0 is 4. Find the value of f(x) at x = 5.
- a)-3.5
- b)-4
- c)-5
- d)4
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
DIRECTIONSfor the question:Solve the following question and mark the b...
Let f(x) = ax2 + bx + c
► F(2) = 10 → 4a + 2b + c = 10
► F(0) = 4 → c = 4.
will be 0, 2ax + b = 0 → 4a + b = 0
► F(2) = 10 → 4a + 2b + c = 10
► F(0) = 4 → c = 4.
will be 0, 2ax + b = 0 → 4a + b = 0
Solving these we get
► a = -1.5
► b = 6
► c = 4.
So, f(x) = -1.5x2 + 6x + 4
at x = 5 gives -3.5.
► a = -1.5
► b = 6
► c = 4.
So, f(x) = -1.5x2 + 6x + 4
at x = 5 gives -3.5.
Free Test
FREE
| Start Free Test |
Community Answer
DIRECTIONSfor the question:Solve the following question and mark the b...
Given:
- A quadratic function f(x) attains a maximum of 10 at x = 2.
- The value of the function at x = 0 is 4.
To Find:
- The value of f(x) at x = 5.
Solution:
To find the value of f(x) at x = 5, we need to determine the equation of the quadratic function f(x).
Step 1: Finding the equation of the quadratic function
Since the quadratic function attains a maximum at x = 2, we know that the vertex of the parabola lies at (2, 10). The vertex form of a quadratic function is given by:
f(x) = a(x - h)^2 + k
where (h, k) represents the vertex of the parabola.
Substituting the values of the vertex (2, 10) into the equation, we have:
f(x) = a(x - 2)^2 + 10
To find the value of 'a', we can use the fact that the value of the function at x = 0 is 4. Substituting these values into the equation, we have:
4 = a(0 - 2)^2 + 10
4 = 4a + 10
-6 = 4a
a = -6/4
a = -3/2
Therefore, the equation of the quadratic function is:
f(x) = (-3/2)(x - 2)^2 + 10
Step 2: Finding the value of f(x) at x = 5
To find the value of f(x) at x = 5, we substitute x = 5 into the equation:
f(5) = (-3/2)(5 - 2)^2 + 10
Simplifying the expression:
f(5) = (-3/2)(3)^2 + 10
f(5) = (-3/2)(9) + 10
f(5) = -27/2 + 10
f(5) = -27/2 + 20/2
f(5) = -7/2
Answer:
The value of f(x) at x = 5 is -7/2, which is equivalent to -3.5. Therefore, the correct answer is option A, -3.5.
- A quadratic function f(x) attains a maximum of 10 at x = 2.
- The value of the function at x = 0 is 4.
To Find:
- The value of f(x) at x = 5.
Solution:
To find the value of f(x) at x = 5, we need to determine the equation of the quadratic function f(x).
Step 1: Finding the equation of the quadratic function
Since the quadratic function attains a maximum at x = 2, we know that the vertex of the parabola lies at (2, 10). The vertex form of a quadratic function is given by:
f(x) = a(x - h)^2 + k
where (h, k) represents the vertex of the parabola.
Substituting the values of the vertex (2, 10) into the equation, we have:
f(x) = a(x - 2)^2 + 10
To find the value of 'a', we can use the fact that the value of the function at x = 0 is 4. Substituting these values into the equation, we have:
4 = a(0 - 2)^2 + 10
4 = 4a + 10
-6 = 4a
a = -6/4
a = -3/2
Therefore, the equation of the quadratic function is:
f(x) = (-3/2)(x - 2)^2 + 10
Step 2: Finding the value of f(x) at x = 5
To find the value of f(x) at x = 5, we substitute x = 5 into the equation:
f(5) = (-3/2)(5 - 2)^2 + 10
Simplifying the expression:
f(5) = (-3/2)(3)^2 + 10
f(5) = (-3/2)(9) + 10
f(5) = -27/2 + 10
f(5) = -27/2 + 20/2
f(5) = -7/2
Answer:
The value of f(x) at x = 5 is -7/2, which is equivalent to -3.5. Therefore, the correct answer is option A, -3.5.
|
Explore Courses for CAT exam
|
|
Top Courses for CATView all
DIRECTIONSfor the question:Solve the following question and mark the best possible option.A quadratic function f(x) attains a maximum of 10 at x = 2. The value of the function at x = 0 is 4. Find the value of f(x) at x = 5.a)-3.5b)-4c)-5d)4Correct answer is option 'A'. Can you explain this answer?
Question Description
DIRECTIONSfor the question:Solve the following question and mark the best possible option.A quadratic function f(x) attains a maximum of 10 at x = 2. The value of the function at x = 0 is 4. Find the value of f(x) at x = 5.a)-3.5b)-4c)-5d)4Correct answer is option 'A'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about DIRECTIONSfor the question:Solve the following question and mark the best possible option.A quadratic function f(x) attains a maximum of 10 at x = 2. The value of the function at x = 0 is 4. Find the value of f(x) at x = 5.a)-3.5b)-4c)-5d)4Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for DIRECTIONSfor the question:Solve the following question and mark the best possible option.A quadratic function f(x) attains a maximum of 10 at x = 2. The value of the function at x = 0 is 4. Find the value of f(x) at x = 5.a)-3.5b)-4c)-5d)4Correct answer is option 'A'. Can you explain this answer?.
DIRECTIONSfor the question:Solve the following question and mark the best possible option.A quadratic function f(x) attains a maximum of 10 at x = 2. The value of the function at x = 0 is 4. Find the value of f(x) at x = 5.a)-3.5b)-4c)-5d)4Correct answer is option 'A'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about DIRECTIONSfor the question:Solve the following question and mark the best possible option.A quadratic function f(x) attains a maximum of 10 at x = 2. The value of the function at x = 0 is 4. Find the value of f(x) at x = 5.a)-3.5b)-4c)-5d)4Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for DIRECTIONSfor the question:Solve the following question and mark the best possible option.A quadratic function f(x) attains a maximum of 10 at x = 2. The value of the function at x = 0 is 4. Find the value of f(x) at x = 5.a)-3.5b)-4c)-5d)4Correct answer is option 'A'. Can you explain this answer?.
Solutions for DIRECTIONSfor the question:Solve the following question and mark the best possible option.A quadratic function f(x) attains a maximum of 10 at x = 2. The value of the function at x = 0 is 4. Find the value of f(x) at x = 5.a)-3.5b)-4c)-5d)4Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT.
Download more important topics, notes, lectures and mock test series for CAT Exam by signing up for free.
Here you can find the meaning of DIRECTIONSfor the question:Solve the following question and mark the best possible option.A quadratic function f(x) attains a maximum of 10 at x = 2. The value of the function at x = 0 is 4. Find the value of f(x) at x = 5.a)-3.5b)-4c)-5d)4Correct answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
DIRECTIONSfor the question:Solve the following question and mark the best possible option.A quadratic function f(x) attains a maximum of 10 at x = 2. The value of the function at x = 0 is 4. Find the value of f(x) at x = 5.a)-3.5b)-4c)-5d)4Correct answer is option 'A'. Can you explain this answer?, a detailed solution for DIRECTIONSfor the question:Solve the following question and mark the best possible option.A quadratic function f(x) attains a maximum of 10 at x = 2. The value of the function at x = 0 is 4. Find the value of f(x) at x = 5.a)-3.5b)-4c)-5d)4Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of DIRECTIONSfor the question:Solve the following question and mark the best possible option.A quadratic function f(x) attains a maximum of 10 at x = 2. The value of the function at x = 0 is 4. Find the value of f(x) at x = 5.a)-3.5b)-4c)-5d)4Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice DIRECTIONSfor the question:Solve the following question and mark the best possible option.A quadratic function f(x) attains a maximum of 10 at x = 2. The value of the function at x = 0 is 4. Find the value of f(x) at x = 5.a)-3.5b)-4c)-5d)4Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice CAT tests.
|
|
Explore Courses for CAT exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup