
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 = x^{2} 
4x on the interval
from x = 1 to x = 5.
x 
x^{2}  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 xaxis are called the roots. The parabola crosses the xaxis 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 = ax^{2} +
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. 
