Question

What is the equation of the parabola that has a vertex at `(3, -6)` and passes through point `(-9,7)`?

Answer 1

`f(x)=13/144(x-3)^2-6`

Explanation:

We know that

`f(x)=a*(x-3)^2-6`

because of the vertex at `(3,-6)`. Now we have to determinated `a` by plugging in the point `(-9,7)`.

`7=a*(-9-3)^2-6`

In order to find `a`, we solve for `a`

`7=a*(-9-3)^2-6|+6`
`13=144a|:144`
`13/144=a~~0.09`