Question

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

Answer 1

the origin is the vertex location, thus (0, 0)
the focus is at (0, -7)

notice, only the "y-coordinate" changed, that means is moving about vertically, up and down
thus the "focus form" equation for that is \(\bf (x-h)^2=4p(y-k)\)

(h, k) = vertex coordinates
p = distance from the vertex to the focus

the focus is below the origin, thus the parabola is going DOWN, it also means the value for the "p" variable will be negative

Answer 2

so, plug your values in and solve for "y"

Answer 3

I got y2 = -7x.

Answer 4

\(\bf y^2 \quad ?\)

the so-called "focus form" doesn't have a squared "y"

Answer 5

Okay, I now have y = negative one divided by sevenx2

Answer 6

hmm, you're forgetting the "4" in front of the "P"

otherwise, you're correct

Answer 7

so the denominator would be 28 and not 7?

Answer 8

yeap

Answer 9

\(\bf (x-h)^2=4p(y-k) \implies (x-0)^2=4(-7)(y-0) \implies x^2 = -28y\\ \implies -\cfrac{1}{28}x^2 = y\)

Answer 10

Thank You !

Answer 11

yw