Question

1. what are the coordinates of the vertex of the quadratic function $y = -2x^2 - 8x + 1$?

a. $(8, 9)$
b. $(9, -2)$
c. $(-8, 1)$
d. $(-2, 9)$

Explanation:

Step1: Find x-coordinate of vertex

For quadratic $y=ax^2+bx+c$, $x=-\frac{b}{2a}$. Here $a=-2$, $b=-8$.
$x=-\frac{-8}{2(-2)}=\frac{8}{-4}=-2$

Step2: Find y-coordinate of vertex

Substitute $x=-2$ into $y=-2x^2-8x+1$.
$y=-2(-2)^2-8(-2)+1=-2(4)+16+1=-8+16+1=9$

Answer:

d. $(-2, 9)$