Question

What is the equation of the parabola shown in the graph?

Answer 1

`{(y + 2)}^(2) = 8(x - 4)`

EXPLANATION

The given parabola has equation of the form

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

where (h,k) is the vertex of the parabola.

The vertex of the given parabola is (4,-2).

and p is the distance between the foci and the vertex.

`|p| = 2`

The parabola opens towards the positive x-axis, therefore p=2.

Hence the equation of the parabola is

`{(y + 2)}^(2) = 4 * 2(x - 4)`

`{(y + 2)}^(2) = 8(x - 4)`

Answer 2

Your answer is going to be E for plato users or (y^2/8) + (y/2) + (9/2)

Explanation:

Since it is a horizontal Parabola the equation is: (y-k)^2 = 4p(x-h)

The distance between the directrix: p

therefore P=2

h = X value in the vertex

k = Y value in the vertex

h = 4

k = -2

Plug the values into the equation and solve for x