Question

What is the equation of the graph below?

A graph shows a parabola that opens up with a vertex at three comma negative two.

Answer 1

`y=(x-3)^2-2`

Explanation:

Given vertex of parabola
`(3,-2)`

Where
`(h,k)` is the vertex.

`(h,k)=(3,-2)\\h=3\ and\ k=-2`

Also parabola opens up.

The equation of parabola with vertex
`(h,k)`

`y= a(x - h)^2 + k`

If
`a>0` parabola opens up.

`a<0` parabola opens down.

As the parabola opens up the value of
`a` will greater than zero.

Plugging vertex of parabola in equation
`y= a(x - h)^2 + k`

`y= a(x - 3)^2 -2`

Let us plug
`a=1`

The equation will be
`y= a(x - 3)^2 -2`