Quadratic graphs - Intermediate and Higher tier - Equations of curves - Intermediate & Higher tier – WJEC - GCSE Maths Revision - WJEC

Quadratic graphs - Intermediate and Higher tier

A quadratic graph is any graph which has an \(\text{x}^2\) in its equation. We draw them in a very similar way to straight-line graphs and will need to substitute values into the equation. All quadratic graphs will be curved.

Example

We want to draw the graph of \(\text{y = x}^2~{+~3}\) so we will need to complete this table of values:

\(\text{x}\)	-3	-2	-1	0	1	2	3
\(\text{y = x}^2~{+~3}\)

\(\text{x}\)
-3
-2
-1
0
1
2
3

\(\text{y = x}^2~{+~3}\)

when x = -3, y = (-3 x -3) + 3 = 12
when x = -2, y = (-2 x -2) + 3 = 7
when x = -1, y = (-1 x -1) + 3 = 4
when x = 0, y = (0 x 0) + 3 = 3
when x = 1, y = (1 x 1) + 3 = 4
when x = 2, y = (2 x 2) + 3 = 7
when x = 3, y = (3 x 3) + 3 = 12

So our completed table of values will look like this:

\(\text{x}\)	-3	-2	-1	0	1	2	3
\(\text{y = x}^2~{+~3}\)	12	7	4	3	4	7	12

\(\text{x}\)
-3
-2
-1
0
1
2
3

\(\text{y = x}^2~{+~3}\)
12
7
4
3
4
7
12

To draw this graph, we need to think of the values in this table as coordinates.

So the first point will have the coordinates \(\text{(-3, 12)}\), the second will have the coordinates \(\text{(-2, 7)}\) etc.

We then join up our points with a curve:

A graph showing the equation y = x squared + 3.

Question

Complete the table and draw the graph of \(\text{y = 2x}^2~{-~1}\).

\(\text{x}\)	-3	-2	-1	0	1	2	3
\(\text{y = 2x}^2~{-~1}\)

\(\text{x}\)
-3
-2
-1
0
1
2
3

\(\text{y = 2x}^2~{-~1}\)

Equations of curves - Intermediate & Higher tier – WJECQuadratic graphs - Intermediate and Higher tier