## Theory

Take a look at the applet: Quadratic Functions

A function of the form $f\left(x\right)=a{\left(x-p\right)}^{2}+q$, is called a quadratic function (if $a\ne 0$).
The graph of a quadratic function can be derived by transformations of the graph of $y={x}^{2}$.
The graph of every quadratic function is a parabola with vertex $\left(p,q\right)$ andaxis of symmetry $x=p$.
If $a>0$ then the parabola will open upwards.
If $a<0$ then the parabola will open downwards.

The quadratic equation $a{\left(x-p\right)}^{2}+q=u$ can be rewritten as: ${\left(x-p\right)}^{2}=c$.

• If $c>0$ there are two solutions.

• If $c=0$ there is only one solution.

• If $c<0$ there are no solutions.

You can find the solutions by using radicals.