2
advanced-math

What are the coordinates of the vertex for y=2x2+8x3y = 2x^2 + 8x - 3?

A

(2,11)(-2, -11)

B

(2,21)(2, 21)

C

(2,3)(-2, -3)

D

(4,3)(-4, -3)

Correct Answer: A

Choice A is the correct answer. The vertex (h,k)(h, k) is found by first calculating the x-coordinate h=b/2ah = -b/2a.

  1. h=8/(2×2)=8/4=2h = -8 / (2 \times 2) = -8 / 4 = -2.
  2. Substitute x=2x = -2 back into the equation to find yy: y=2(2)2+8(2)3y = 2(-2)^2 + 8(-2) - 3y=2(4)163y = 2(4) - 16 - 3y=8163=11y = 8 - 16 - 3 = -11.

So the vertex is (2,11)(-2, -11).

Choice B is incorrect because it uses x=2x=2. Choice C is incorrect because it assumes the y-intercept (-3) is the y-coordinate of the vertex. Choice D is incorrect because it calculates x incorrectly.