Question

What is the equation of the parabola that has a vertex at `(-5, -4)` and passes through point `(5,396)`?

Answer 1

`y = 4x^2 +40x +96`

Explanation:

The equation of a parabola, written in vertex form, is `y = n(x - h)^2 +k` where (h,k) are the coordinates of the vertex.
For this example then, `y = n(x+5)^2 -4`
To find n, we substitute in the coordinates of the given point.
`396 = n(5 +5)^2 -4`
`400 = 100n`
`n = 4`
Thus the equation is `y = 4(x+5)^2 -4`
or in standard form `y = 4x^2 +40x +96`