Question

How do you write a quadratic equation with vertex; ( -2,1 ); point: ( 1,-8 )?

Answer 1

`y=7/9(x+2)^2+1`

Explanation:

The general vertex form for a quadratic with vertex at `(color(red)a,color(blue)b)` is
`color(white)("XXX")y=color(green)m(x-color(red)a)^2+color(blue)b`
(where `color(green)m` can be thought of as a "spread" factor).

Given the vertex `(color(red)(-2),color(blue)1)`
this becomes
`color(white)("XXX")y=color(green)m(x-(color(red)(-2)))^2+color(blue)1=color(green)m(x+2)^2+1`

If `(x,y)=(1,8)` is a solution to this equation,
then
`color(white)("XXX")8=color(green)m(1+2)^2+1`

`color(white)("XXX")rarr 7=color(green)mxx9`

`color(white)("XXX")rarr color(green)m=color(green)(7/9)`

and the complete quadratic is
`color(white)("XXX")y=color(green)(7/9)(x+2)^2+1`