How do you find the equation of a parabola with vertex at the origin and directrix y=-1?

1 Answer
Sep 2, 2017

Answer:

Equation of parabola is #y=1/4x^2#

Explanation:

Vertex is at #(0,0)# , Directrix is #y=-1#

Equation of parabola is # y= a(x-h)^2 + k ; (h,k) # being vertex.

# y= a(x-0)^2+0 or y = ax^2 # . Directrix is below the vertex ,

so parabola opens upward and #a# is positive . The distance of

directrix from vertex is#D=1 # , We know # D= 1/(4|a|)# or

#1= 1/(4|a|) or a = 1/4# . Equation of parabola is #y=1/4x^2#

graph{1/4 x^2 [-12.66, 12.65, -6.33, 6.33]} [Ans]