Question

Write the equation in standard form for the parabola with vertex (0,0) and directrix y=-6

Answer 1

what is the distance between the vertex and directrix...?

Answer 2

the general equation I use is

\[(x -h)^2 = 4a(y - k)\]

(h, k) is the vertex and a is the focal length

the focal length is the distance between the directrix and vertex..

because the directrix is below the vertex, I know the parabola is concave up

so when you find a

substitute a, h = 0, k = 0 and then simplify to find the equation