Completing the square
Any quadratic function ax2 + bx + c can be written
in the form a (x - h)2 + constant. In fact, we have
ax2 + bx + c = a[x + b/(2a)]2
+ c - b2/(4a2).
The animation below shows an example of this conversion from one
form to another, and the applet lets you try some examples. When you
fill in a field in the applet, enter either a fraction like -1/4 or an integer
like 3.
Animation of the method
Tutorial applet