QUADRATIC GRAPHS

Tables of values

For more complicated quadratic graphs it is expected that a table of values needs to be used in order to work out the y co-ordinates.

A table of values simply organises the calculation in a more effective way.

Example:Draw the graph of y = x2 – 6 ; for x between – 3 and + 3.

X - 3 - 2 - 1 0 1 2 3x2

- 6 y

9 4 1 0 1 4 9 - 6 - 6 - 6 - 6 - 6 - 6 - 6

3 - 2 - 5 - 6 - 5 - 2 3

Draw a suitable pair of axes and plot the parabola.

1 2 3-1-2-3x

-5

-4

-3

-2

-1

-6

1

2

3 yx

x

x

x

xx

x

x -3 -2 -1 0 1 2 3y = x2- 6 3 - 2 - 5 - 6 - 5 - 2 3

Example:Draw the graph of y = x2 – 4x ; for x between – 1 and + 5.

X - 1 0 1 2 3 4 5x2

- 4x y

1 0 1 4 9 16 25

Draw a suitable pair of axes and plot the parabola.

4 - 0 - 4 - 8 - 12 - 16 - 20

5 0 - 3 - 4 - 3 0 5

3

2

4-1

1-1

x

- 4

-2

-3

2

1

3

4

5yx

x

x

x

xx

x

5

X - 1 0 1 2 3 4 5y 5 0 - 3 - 4 - 3 0 5

Example:Draw the graph of y = x2 + 2x ; for x between – 4 and + 2.

X - 4 - 3 - 2 - 1 0 1 2x2

2x y

16 9 4 1 0 1 4

Draw a suitable pair of axes and plot the parabola.

- 8 - 6 - 4 - 2 0 2 4

8 3 0 - 1 0 3 8

- 4 - 1 2

8

x

y

X - 4 - 3 - 2 - 1 0 1 2y 8 3 0 - 1 0 3 8