Question

Write the equation in vertex form for the parabola with vertex ( 0, - 4 ) and focus ( 0, - 5 ) .

Answer 1

This parabola is a vertical one, symmetrical about the y-axis.  It opens DOWN.  We know that because the focus is beneath the vertex.

We need to write this equation in the form y-k = 4p(x-h)^2, where (h,k) is the vertex.  p represents the distance between the vertex and the focus, and is 
|-4-(-5)|, or 1.

Thus, y-(-4) = 4(1)(x-0)^2, or y+4 = 4x^2.