Question

What is the equation of the following graph?

Answer 1

From the diagram, Vertex =(2,3)

So, (h,k)=(2,3)

So, h=2 and k=3

The equation of parabola is

$(x-h)^{2}=4p(y-k)$

p is the distance of directrix or focus from vertex.

As directrix is

y=8=k-p=3-p

So, 8=3-p

Let, us subtract 3 from both sides, we get

8-3=3-3-p

5=-p

or p=-5

So, h=2,k=3 and p=-5

So, the equation of parabola is

$(x-2)^{2}$=4(-5)(y-3)

Equation of graph is

(x-2)^2=-20(y-3)