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Math
A |
Graphs of
Parabolas |
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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 |
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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).
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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.
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Parabolas are of
the form: y = ax2 + bx + c |
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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. |
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