6
advanced-math

A rectangle is inscribed in an isosceles triangle. The area of the rectangle is modeled by A(x)=−2x2+12xA(x) = -2x^2 + 12x. What x-value maximizes the area?

A

3

B

6

C

2

D

4

Correct Answer: A

Choice A is the correct answer. Find the vertex of the quadratic function.

  1. x=−b/2ax = -b/2a.
  2. x=−12/(2(−2))=−12/−4=3x = -12 / (2(-2)) = -12 / -4 = 3.

Choice B is incorrect. Choice C is incorrect. Choice D is incorrect.

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Set 19: Quadratic Equations and Functions 19