Plotting graphs

A graph question nearly always starts with a table of values. Work out y for each x, one column at a time.

1. write the equation with y on its own: 2y = 3x − 2 becomes y = (3x − 2) ÷ 2
2. put each x in brackets when it is negative: x = −2 gives y = (3 × (−2) − 2) ÷ 2 = −4
3. for x², square first: (−3)² = 9, never −9
4. check the pattern: a straight line goes up or down by the same amount each step

The usual slip: (−3)² typed into a calculator as −3² gives −9. Use the brackets.

Plot each point as a small cross, to within half a small square. Then join the points the way the equation says:

• a straight line (y = mx + c, or ax + by = c) with a ruler, right across the grid;
• a curve (x², x³, k/x, 2^x) with one smooth curve through every point, never with straight pieces between them.

A quadratic is symmetrical, so its lowest point sits halfway between two points with the same y value. If one point breaks the pattern, recheck it before you draw.

Once the graph is drawn, it answers questions.

1. x² − 4x + 1 = 0: read the x values where the curve crosses the x-axis (y = 0)
2. x² − 4x + 1 = 4: draw the line y = 4 and read the x values where it meets the curve
3. a value off the end of a straight-line graph: read a value you can reach, then scale it up

Give a reading to the accuracy the grid allows, usually 1 decimal place. A mark scheme accepts a small range either side of the true value.