Question

How do you write a quadratic equation with vertex; ( 2,-2 ); point: ( 4,10 )?

Answer 1

The vertex form of a quadratic with vertex `(h,k)` looks like this:

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

In this case, we already know `h = 2` and `k=-2`, so our equation is:

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

So all we have to do is find `a`. We can do this by plugging in the other point `(color(red)4,color(blue)10)` we were given (which we know works since it is on the parabola) and solving for `a`.

`color(blue)10 = a(color(red)4-2)^2-2`

`10 = a*2^2 - 2`

`10 = 4a-2`

`12 = 4a`

`3 = a`

Therefore, our equation is:

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

Final Answer