4

Set 9: Quadratic Equations (Advanced)

Explanation

Answer: A

If f(x)=ax2+bx+cf(x) = ax^2 + bx + c has roots −2-2 and 44, and a maximum value of 18, find the equation.

A.

y=−2(x+2)(x−4)y = -2(x + 2)(x - 4)

✓ Correct
B.

y=2(x+2)(x−4)y = 2(x + 2)(x - 4)

C.

y=−(x+2)(x−4)y = -(x + 2)(x - 4)

D.

y=−2(x−2)(x+4)y = -2(x - 2)(x + 4)

Detailed Explanation

Choice A is correct. Choice A is the correct answer. 1. Roots Form: y=a(x+2)(x−4)y = a(x + 2)(x - 4). 2. Find Vertex x: Midpoint of roots: (−2+4)/2=1(-2 + 4) / 2 = 1. 3. Find a: Vertex is (1,18)(1, 18). Substitute into equation. 18=a(1+2)(1−4)18=a(3)(−3)18=−9a⇒a=−218= a(1 + 2)(1 - 4)18= a(3)(-3)18= -9 a \Rightarrow a = -2. 4. Equation: y=−2(x+2)(x−4)y = -2(x + 2)(x - 4). Choice B is incorrect. Choice C is incorrect. Choice D is incorrect.

Key Steps:

•

The correct answer is y=−2(x+2)(x−4)y = -2(x + 2)(x - 4)

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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