Question

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

y=−18x2−2x−4

Answer 1

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

Explanation:

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

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

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

`((16)/(2))^2=64`

Add 64 in the space you made, then compensate for that at the end of the expression by subtracting
`-(1)/(8)(64)=-8`

`y=-(1)/(8)(x^2+16x+64)-4+8\\y=-(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)

Answer 2

The coordinates of the focus of the parabola is (-8, 2)

How to find the coordinates of the focus

To find the coordinates of the focus of the parabola given by the equation y = -1/8x² - 2x - 4, we use the standard form of a parabola

y = -ax² + bx + c

The coordinates of the focus are given by (h, k), where

h = -b / 2a and

k is the y-coordinate of the vertex.

For your equation

h = -(-2) / ( 2 * -1/8)

h = -8

solving for k

k = -1/8(-8)² - 2(-8) - 4

k = -8 + 16 - 4

k = 4

The coordinates of the vertex is (-6, 4). The coordinates of the focus in this case is (h, k + 1/4a). Hence we have

(-8, 4 + 1/4(-1/8)

(-8, 4 + 1/(-1/2)

(-8, 4 + (-2))

(-8, 2)

So, the coordinates of the focus are (-8, 2)