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.
| x | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| 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
| x | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| y = x2 + 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 = 2x2 - 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 = 2x2 - 10. -8 8 40 62
- Answer
Here's how the completed table looks:
x 0 1 2 3 4 5 6 y = 2x2 - 10. -10 -8 -2 8 22 40 62 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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