Question

Find h, k, and p

Write the equation in standard form
Identify the missing pieces

Vertex (0,0); focus (0,-4)

Answer 1

Explanation:

This is a parabola. If we plot the vertex and the focus, we see that the focus is below the vertex. What this tells us is that the parabola opens "upside down" since the parabola wraps itself around the focus. If it opens upside down, then the format for the equation is

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

where p is the distance between the vertex and the focus (4), h is the first coordinate of the vertex (0), and k is the second coordinate of the vertex (0). Filling in the formula then:

`4(4)(y-0)=-(x-0)^2` which simplifies down to

`16y=-x^2` and then finally,

`y=-(1)/(16)x^2`