Question

PLEASE ANSWER QUICK 25 ACTUAL POINTS!

Find the standard form of the equation of the parabola with a vertex at the origin and a focus at (0, -7).


(Answer choices are in picture)

Answer 1

The vertex of the parabola is at (0,0), and the focus is at (0,-7). 

The focus is given by the following values:

$(h, k + p)$

h and k represent the x and y values of the vertex. We want to solve for p.

Set the y value for the focus equal to -7:

$k + p = -7$

We know that k = 0, so we can simplify to get p by itself:

$p = -7$

Standard form of a vertical parabola is given by the following formula:

$(y - k)^2 = 4p(x - h)$

Plug in all of your known values into the formula:

$h = 0, k = 0, p = -7$

$(y - 0)^2 = 4(-7)(x - 0)$
$y^2 = -28x$

The answer is "y^2 = -28x".

Answer 2

Formula for parabola with focus at (0,p) and vertex at origin $y^2 = 4px$

Since focus is at (0,-7), p = -7 and $y^2 = -28x$