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Graphs of quadratic Graphs of quadratic functionsfunctions
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Plotting graphs of quadratic functions
Plot the graph of y = x2 – 4x + 2 for –1 < x < 5.
We can plot the graph of a quadratic function using a table of values. For example:
x
x2
– 4x
+ 2
y = x2 – 4x + 2
–1 0 1 2 3 4 5
1 0 1 4 9 16 25
+ 4 + 0 – 4 – 8 – 12 – 16 – 20
+ 2 + 2 + 2 + 2 + 2 + 2 + 2
7 2 –1 –2 –1 2 7
y = ax2 + bx + c (where a ≠ 0)A quadratic function in x can be written in the form:
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x
1
0 1–1 3 4 5–1
2
3
4
5
6
y
2
Plotting graphs of quadratic functions
x
y = x2 – 4x + 2
–1 0 1 2 3 4 5
7 2 –1 –2 –1 2 7
The points given in the table are plotted …
… and the points are then joined together with a smooth curve.
The shape of this curve is called a parabola.
It is characteristic of a quadratic function.
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Parabolas
When the coefficient of x2 is positive the vertex is a minimum point and the graph is -shaped.
When the coefficient of x2 is negative the vertex is a maximum point and the graph is -shaped.
Parabolas have a vertical axis of symmetry …
…and a turning point called the vertex.
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Graphs of the form y = ax2 + bx + c