3
advanced-math

Find the vertex of y=x2−8x+12y = x^2 - 8x + 12.

A

(4,−4)(4, -4)

B

(−4,60)(-4, 60)

C

(4,4)(4, 4)

D

(−4,−4)(-4, -4)

Correct Answer: A

Choice A is the correct answer. The x-coordinate of the vertex is given by h=−b/2ah = -b/2a.

  1. Identify: a=1,b=−8a=1, b=-8.
  2. Calculate h: h=−(−8)/2(1)=8/2=4h = -(-8) / 2(1) = 8 / 2 = 4.
  3. Calculate k: Substitute x=4x=4 back into the equation. y=42−8(4)+12=16−32+12=−4y = 4^2 - 8(4) + 12 = 16 - 32 + 12 = -4.

So the vertex is (4,−4)(4, -4).

Choice B is incorrect because it uses x=−4x=-4. Choice C is incorrect because of a sign error in calculation (16−32+12eq416-32+12 eq 4). Choice D is incorrect because it uses x=−4x=-4.

Next
Question 4 →
Back to Set
Set 5: Quadratic Equations and Functions 5