Graphs of Parabolas

Math A

Graphs of Parabolas

An easy method for graphing parabolas involves preparing a chart.
Of course, the graphing calculator can also be used.

Example:

Graph the parabola y = x² - 4x
on the interval from x = -1 to x = 5.

x x2 - 4x y -1 (-1)2 - 4(-1) 5 0 (0)2 - 4(0) 0 1 (1)2 - 4(1) -3 2 (2)2 - 4(2) -4 3 (3)2 - 4(3) -3 4 (4)2 - 4(4) 0 5 (5)2 - 4(5) 5

Plot the points generated in the table. Draw a smooth curve through the points. The points where the graph crosses the x-axis are called the roots. The parabola crosses the x-axis at (0,0) and (4,0).

The axis of symmetry is a vertical line passing through the turning point of a parabola.

In this example the turning point is (2,-4).
The equation of the axis of symmetry is x = 2.

Parabolas are of the form: y = ax2 + bx + c

If a is positive, the parabola opens upward and has a minimum point. The axis of symmetry is x = (-b)/2a	If a is negative, the parabola opens downward and has a maximum point. The axis of symmetry is x = (-b)/2a.