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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