Drawing a curved graph is similar to drawing a straight-line graph and you also have to substitute numbers into the equation.

With a curved line graph the formula will include x^{2}, or some other power of x.

For a curved graph, you need as many points as possible to make it accurate.

Complete the table for y = x^{2} + 2.

x | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |

y = x^{2} + 2 |

We know that y = x^{2} + 2, so we need to square (multiply by itself) each x value and add 2.

- If x = 0, y = 0 × 0 + 2 = 2
- If x = 1, y = 1 × 1 + 2 = 3
- If x = 2, y = 2 × 2 + 2 = 6
- If x = 4, y = 4 × 4 + 2 = 18
- If x = 5, y = 5 × 5 + 2 = 27
- If x = 7, y = 7 × 7 + 2 = 51

This can be used to complete a table

x | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |

y = x^{2} + 2 | 2 | 3 | 6 | 11 | 18 | 27 | 38 | 51 |

We could plot these points on a grid. Each pair of values is an (x, y) coordinate - eg, (0, 2), (1, 3), (2, 6) etc.

- Question
Complete the table for y = 2x

^{2}- 10. Then draw the graph for the equation.Use your graph to find the value of x when y = 15

x 0 1 2 3 4 5 6 y = 2x ^{2}- 10.-8 8 40 62

- Answer
Here's how the completed table looks:

x 0 1 2 3 4 5 6 y = 2x ^{2}- 10.-10 -8 -2 8 22 40 62 Draw the graph of y = 2x

^{2}- 10.The value of x when y = 15 should be about 3.5.

Now practise drawing some more curved graphs in the activity below.

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