Question

How do you write the equation of the parabola in vertex form given the vertex (9,-2) and point (12,16)?

Answer 1

`y=2(X-9)^2-2`

Explanation:

The general vertex form is
`color(white)("XXX")y=m(x-a)^2+b` for a parabola with vertex at `(a,b)`

So a parabola with vertex at `(9,-2)` will have the form:
`color(white)("XXX")y=m(x-9)^2+(-2)`

Since `(x,y)=(12,16)` is given as a solution to this equation
`color(white)("XXX")16=m(12-9)^2-2`

`color(white)("XXX")16=9m-2`

`color(white)("XXX")m=2`
and
the equation of the parabola is
`color(white)("XXX")y=2(x-9)^2-2`
graph{2(x-9)^2-2 [1.37, 13.854, -2.37, 3.87]}