8
advanced-math

What is the maximum value of the function f(x)=−3x2+12x−5f(x) = -3x^2 + 12x - 5?

A

7

B

-5

C

12

D

2

Correct Answer: A

Choice A is the correct answer.

  1. Find Vertex x: x=−b/2a=−12/(2(−3))=2x = -b/2a = -12 / (2(-3)) = 2.
  2. Find Max Value: Substitute x=2x=2 into f(x)f(x). f(2)=−3(2)2+12(2)−5f(2) = -3(2)^2 + 12(2) - 5f(2)=−12+24−5=7f(2) = -12 + 24 - 5 = 7.

Choice B is incorrect because it is the y-intercept. Choice C is incorrect. Choice D is incorrect because it is the x-coordinate.

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