Question

What is the equation of the parabola that has a vertex at `(-11, 3)` and passes through point `(13,5)`?

Answer 1

`576y = 2(x+11)^2 + 1728`

Explanation:

The vertex form of a parabola is `y = a(x-b)^2 +c` where the vertex is `(b,c)`
Therefore `y = a(x+11)^2 +3`
By using the coordinates of the given point we can find a
`5 = a(13 + 11)^2 +3`
`a = (5-3)/24^2 = 2/576`

`576y = 2(x+11)^2 + 1728`