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# Curved graphs

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 x2, or some other power of x.

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

## Example

Complete the table for y = x2 + 2.

x01234567
y = x2 + 2

We know that y = x2 + 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

x01234567
y = x2 + 22361118273851

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 = 2x2 - 10. Then draw the graph for the equation.

Use your graph to find the value of x when y = 15

x0123456
y = 2x2 - 10.  -8 8 4062

Here's how the completed table looks:

x0123456
y = 2x2 - 10. -10-8-28224062

Draw the graph of y = 2x2 - 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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