Question

Find the standard form of the equation of the parabola with a vertex at the origin and a focus at (0, -4).

Answer 1

please help me @Albert0898

Answer 2

do you know what vertex form for a parabola looks like?

Answer 3

http://www.mathwarehouse.com/geometry/parabola/standard-to-vertex-form.php

Answer 4

how do we make it standard form tho

Answer 5

wait wait is it -1/16x^2=y

Answer 6

thats not one of my choices

Answer 7

y = -1/4x^2
y2 = -4x
y2 = -16x
y = -1/16x^2

Answer 8

you haven't found the value of \(a\) yet, which depends on the location of the focus.

Answer 9

how

Answer 10

are you sure?

Answer 11

Yes, I'm sure you need to find the value of \(a\) because there are an infinite number of parabolas with a vertex at the origin, but only one with a focus at \((0,-4)\), and the value of \(a\) is what separates the wrong ones from the one you need.

You have two answer choices which have a \(y^2\) term instead of a \(y\) term. You can reject those out of hand, as they represent parabolas which open to the side (along the x-axis) instead of up or down (along the y-axis).

Answer 12

@alejandranunez

To find the correct equation, we use the formula \[(x-h)^2 = 4p(y-k)\]where \((h,k)\) is the location of the vertex. We have the vertex at the origin, or \((0,0)\), so that gives us \(h = 0\) and \(k = 0\) and our equation simplifies to
\[(x-0)^2 = 4p(y-0)\]\[x^2 = 4py\]
Now, \(p\) has the same magnitude as the distance between the vertex and the focus. Our focus is at \((0,-4)\) and our vertex is at \((0,0)\) so the distance between them is \(4\). That means that either \(p = 4\) or \(p = -4\). We can figure that out by remembering that the parabola "wraps around" the focus.