10
advanced-math

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)

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)

Correct Answer: A

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(1 + 2)(1 - 4)18=a(3)(−3)18 = a(3)(-3)18=−9a⇒a=−218 = -9a \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.

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Set 20: Quadratic Equations and Functions 20