Take a look at the applet: Quadratic Functions
A function of the form
$f\left(x\right)=a{(x-p)}^{2}+q$, 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
$(p,q)$ 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 $a{(x-p)}^{2}+q=u$ can be rewritten as: ${(x-p)}^{2}=c$.
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.