# Parabolas

The general form of a parabola is:

ax^2+bx+c=y

And may look like the following graph:

If  y=0  (i.e. where the parabola passes through the  axis), then

ax^2+bx+c=0

We have various ways to work out these points (or roots).

You often get asked in an exam to solve a quadratic equation like

3x^2-7x+2=0

This really means that you find the roots of the curve.

The way to solve x (or find the roots) include:

1. Substituting values of x and drawing a curve

2. Completing the square

If you find the value of x at the half way point and plug this value back into ax^2+bx+c=y  this will provide you with the value of y at the turning point.
ax^2+bx+c=y
if you can work out the roots of x  you can plot several points of a parabola (including root1, root2 and the turning point (x,y)\).