Question

Find the vertex, focus, and directrix of the parabola and sketch its graph. Use a graphing utility to verify your graph.

y^2-4x-12=0

Answer 1

y^2-4x-12=0
given the form of the ecuation of the parabola (y-k)^2=4p(x-h) where (h,k) is the vertex and p is the distance from the vertice to the focus
y^2=4x+12 ... Factoring 4
y^2=4(x+3)
(y-0)^2=4(x-(-3))
here you can see:
Vertex: (-3,0)
Distance from the vertice to the focus and to the directriz: 4p=4 -> p=1

Answer 2

Thank you so much! Very informative.

Answer 3

So the focus would be (-3,1) and the directrix would be y=3?

Answer 4

directrix is y = -1

Answer 5

sorry for the late