Sketching Graphs Worksheet

Sketching graphs at a glance

In GCSE maths there are a number of different graphs that you need to know and be able to sketch. These include the following graphs: linear graphs, quadratic graphs, cubic graphs, reciprocal graphs, exponential graphs and trigonometric graphs. 

When sketching graphs, we don’t need to accurately plot the graph and therefore we don’t label the axes. What we do do is mark on key points such as intersections with the x axis and y axis and coordinates of the turning points.

 When sketching a graph, we first identify the shape of the graph. For example, a linear graph is a straight line and a quadratic graph is a parabola. We then identify the key points for that graph. For example, when sketching quadratic graphs, we can find the point of intersection with the y axis by substituting x=0 and finding y. We can then find the points of intersection with the x axis by setting y=0 and solving the quadratic equation. If the discriminant of the quadratic (b^{2}-4ac) is less than zero, we won’t be able to solve the equation meaning the graph does not intersect the x axis. Finally, we can complete the square to find the coordinates of the turning point of the quadratic function. 

The exact process will vary depending on the type of graph we are being asked to sketch.

Looking forward, students can then progress to additional interpreting graphs worksheets and other algebra worksheets, for example a sequences worksheet, simultaneous equations worksheet or straight line graphs worksheet.

For more teaching and learning support on Algebra our GCSE maths lessons provide step by step support for all GCSE maths concepts.