Question

NEED THE ANSWER ASAP, PLEASE HELP!! What are the coordinates of the focus of the parabola?

Answer 1

Answer:

Vertex is (-8, 4)  not one of the answers offered!

Step-by-step explanation:

Factor -1/8 out of the first two terms. Leave a space inside parentheses in which to add a number.

$y=-\frac{1}{8}(x^2 + 16x + \text{-----})-4$

Complete the square by squaring half the coefficient of x and adding it in the space.

$(\frac{16}{2})^2=64$

Add 64 in the space you made, then compensate for that at the end of the expression by subtracting  $-\frac{1}{8}(64)=-8$

$y=-\frac{1}{8}(x^2+16x+64)-4+8\\y=-\frac{1}{8}(x+8)^2+4$

The x-coordinate of the vertex is the opposite of +8, the number inside the parentheses.  The y-coordinate of the vertex is the number at the end of the expression.

V(-8, 4)