6

Set 12: Quadratic Equations (Advanced)

Explanation

Answer: A

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

✓ Correct
B.

6

C.

2

D.

4

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Find the vertex of the quadratic function. 1. x=−b/2ax = -b/2 a. 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.

Key Steps:

•

The correct answer is 3

Why others are wrong:
B: Choice B is incorrect and may result from a calculation error.
C: Choice C is incorrect and may result from a calculation error.
D: Choice D is incorrect and may result from a calculation error.
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