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An equation of the form y = ax² + bx + c  ( a does not equal 0 ) defines a quadratic function. To graph a quadratic function select several values of x and then find the corresponding values of y. Graph the ordered pairs and finally draw a smooth curve through the points.

Any equation of the form y = ax² + bx + c has a graph that is a porabola. The point at which the porabola turns is called the vertex. Porabolas are symmetric with respect to a line called the axis of symmetry which contains the vertex. The axis of symmetry lies halfway between any two points with the same y - coordinate. Each function has a minnimum value, a minumum point, a maximum value, and a maximum point.

Example:
The graph of y = -x² + 6x - 5 would look like this:

If you worked the equation out using the numbers 0 - 6 as values for x then the 6 ordered pairs you would obtain would be: (0 , -5) (1 , 0) (2 , 3) (3 , 4) (4 , 3) (5 , 0) and (6 , -5)
In this example, the vertex ( 3 , 4 ) is the maximum point and the vertex (4) is the maximum value. Since the coefficient of x² happens to be a negative 1, the porabola opens downward.

The green line represents the axis of
symmetry for this example.