How do you write the equation of the parabola in vertex form given vertex (0,0) and the directrix y=-16?

1 Answer
Nallasivam V
Jul 2, 2017

#y=1/64 x^2#

Explanation:

Given -

Vertex #(0, 0)#
Directrix #(y=-16)#
Focus #(0,16)#

The Parabola is opening up, as its directrix is #y=-16#

The formula for the parabola in the vertex form is -

#(x-h)^2=4.a.(y-k)^2#

Where -

#h = 0# x-coordinate of the vertex
#k=0# y-coordinate of the vertex
#a=16# distance between vertex and focus

#x-0)^2=4xx16(y-0)#
#x^2=64y#
#y=1/64 x^2#

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