Question

How do you find the quadratic function with vertex (-2,-2) and point (-1,0)?

Answer 1

Function is `y=2(x+2)^2-2=2x^2+8x+6`

Explanation:

A quadratic function written in the form of `y=a(x-h)^2+k`, then the vertex is the point `(h,k)`

As the vertex is `(-2.-2)`, the function is

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

or `y=a(x+2)^2-2`

and as it passes through `(-1,0)`, we have

`0=a(-1+2)^2-2`

or `axx1=2` i.e. `a=2`

Hence, function is `y=2(x+2)^2-2=2x^2+8x+6`
graph{2x^2+8x+6 [-10, 10, -5, 5]}