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

Jun 10, 2017

The vertex form of a quadratic with vertex $\left(h , k\right)$ looks like this:

$y = a {\left(x - h\right)}^{2} + k$

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

$y = a {\left(x - 2\right)}^{2} - 2$

So all we have to do is find $a$. We can do this by plugging in the other point $\left(\textcolor{red}{4} , \textcolor{b l u e}{10}\right)$ we were given (which we know works since it is on the parabola) and solving for $a$.

$\textcolor{b l u e}{10} = a {\left(\textcolor{red}{4} - 2\right)}^{2} - 2$

$10 = a \cdot {2}^{2} - 2$

$10 = 4 a - 2$

$12 = 4 a$

$3 = a$

Therefore, our equation is:

$y = 3 {\left(x - 2\right)}^{2} - 2$