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A quadratic function f(x) attains a maximum of 3 at x = 1. The value of the function at x = 0 is 1. What is the value of f(x) at x = 10 ?
- a)-119
- b)-159
- c)-110
- d)-180
- e)-105
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A quadratic function f(x) attains a maximum of 3 at x = 1. The value o...
We have f(x)=ax^2+bx+cf(x)=ax^2+bx+c.
f(0)=c=1f(0)=c=1 --> f(x)=ax^2+bx+1f(x)=ax^2+bx+1
We are told that fmax(1)=a+b+1=3
, --> a+b=2.
fmax is vertex of parabola and the x coordinate of vertex is
−b/2a=1−b2a=1
--> b=−2a
--> a+b=a
−2a=−a + b =a−2a=
−a=2 --> a=−2a=−2 and b=4b=4.
f(x)=−2x^2+4x+1 =f(x)=−2x^2+4x+1 --> f(10)=−200+40+1=−159
Most Upvoted Answer
A quadratic function f(x) attains a maximum of 3 at x = 1. The value o...
Given information:
- The quadratic function f(x) attains a maximum of 3 at x = 1.
- The value of the function at x = 0 is 1.
To find:
The value of f(x) at x = 10.
Solution:
To find the value of f(x) at x = 10, we need to determine the equation of the quadratic function first.
Step 1: Determine the vertex form of the quadratic function.
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.
Given that the maximum value of f(x) is 3 at x = 1, we can determine the vertex of the parabola using the formula h = -b/2a, where a and b are coefficients of the quadratic function.
Since the maximum value occurs at x = 1, the vertex form can be written as:
f(x) = a(x - 1)^2 + 3
Step 2: Use the given information to find the equation of the quadratic function.
We are given that f(0) = 1. Substituting x = 0 in the equation of the quadratic function, we have:
1 = a(0 - 1)^2 + 3
1 = a + 3
a = -2
Therefore, the equation of the quadratic function is:
f(x) = -2(x - 1)^2 + 3
Step 3: Find the value of f(x) at x = 10.
Substituting x = 10 in the equation of the quadratic function, we have:
f(10) = -2(10 - 1)^2 + 3
f(10) = -2(9)^2 + 3
f(10) = -2(81) + 3
f(10) = -162 + 3
f(10) = -159
Therefore, the value of f(x) at x = 10 is -159.
Hence, the correct answer is option B) -159.
- The quadratic function f(x) attains a maximum of 3 at x = 1.
- The value of the function at x = 0 is 1.
To find:
The value of f(x) at x = 10.
Solution:
To find the value of f(x) at x = 10, we need to determine the equation of the quadratic function first.
Step 1: Determine the vertex form of the quadratic function.
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.
Given that the maximum value of f(x) is 3 at x = 1, we can determine the vertex of the parabola using the formula h = -b/2a, where a and b are coefficients of the quadratic function.
Since the maximum value occurs at x = 1, the vertex form can be written as:
f(x) = a(x - 1)^2 + 3
Step 2: Use the given information to find the equation of the quadratic function.
We are given that f(0) = 1. Substituting x = 0 in the equation of the quadratic function, we have:
1 = a(0 - 1)^2 + 3
1 = a + 3
a = -2
Therefore, the equation of the quadratic function is:
f(x) = -2(x - 1)^2 + 3
Step 3: Find the value of f(x) at x = 10.
Substituting x = 10 in the equation of the quadratic function, we have:
f(10) = -2(10 - 1)^2 + 3
f(10) = -2(9)^2 + 3
f(10) = -2(81) + 3
f(10) = -162 + 3
f(10) = -159
Therefore, the value of f(x) at x = 10 is -159.
Hence, the correct answer is option B) -159.
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A quadratic function f(x) attains a maximum of 3 at x = 1. The value of the function at x = 0 is 1. What is the value of f(x) at x = 10 ?a)-119b)-159c)-110d)-180e)-105Correct answer is option 'B'. Can you explain this answer?
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A quadratic function f(x) attains a maximum of 3 at x = 1. The value of the function at x = 0 is 1. What is the value of f(x) at x = 10 ?a)-119b)-159c)-110d)-180e)-105Correct answer is option 'B'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about A quadratic function f(x) attains a maximum of 3 at x = 1. The value of the function at x = 0 is 1. What is the value of f(x) at x = 10 ?a)-119b)-159c)-110d)-180e)-105Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A quadratic function f(x) attains a maximum of 3 at x = 1. The value of the function at x = 0 is 1. What is the value of f(x) at x = 10 ?a)-119b)-159c)-110d)-180e)-105Correct answer is option 'B'. Can you explain this answer?.
A quadratic function f(x) attains a maximum of 3 at x = 1. The value of the function at x = 0 is 1. What is the value of f(x) at x = 10 ?a)-119b)-159c)-110d)-180e)-105Correct answer is option 'B'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about A quadratic function f(x) attains a maximum of 3 at x = 1. The value of the function at x = 0 is 1. What is the value of f(x) at x = 10 ?a)-119b)-159c)-110d)-180e)-105Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A quadratic function f(x) attains a maximum of 3 at x = 1. The value of the function at x = 0 is 1. What is the value of f(x) at x = 10 ?a)-119b)-159c)-110d)-180e)-105Correct answer is option 'B'. Can you explain this answer?.
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