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.