Quadratic functions look like this: $f(x)=ax^2+bx+c$

The shape of a quadratic graph $y=f(x)$ is called a parabola.

The value of a determines the shape of the parabola.

When $a>0$, the parabola will have a "u" shape.

mtaimg/images/topics/2/2-8-1.png[/mtaimg]/col

When $a<0$, the parabola will have a "n" shape.

mtaimg/images/topics/2/2-8-2.png[/mtaimg]/col

The graph crosses the x-axis (color=redr/color) when $y=0$. These are known as the x-intercepts, and can be calculated by finding the roots of the function f(x).

The graph crosses the y-axis (color=redc/color) when $x=0$. This is known as the y-intercept, and is equal to the value of c.

The turning point (maximum or minimum) of the graph (color=redm/color) is halfway between the two roots, because of the symmetry of the parabola. You can also find the turning point by completing the square.

If $f(x)=a(x-p)^2+q$, the graph $y=f(x)$ has a turning point at $(p,q)$.