Algebra > Quadratics > Sketching Quadratic Graphs
Sketching quadratic graphs helps students connect equations, roots, intercepts and turning points visually.
Key ideas
The sign of the x² coefficient determines whether the parabola opens upwards or downwards.
Roots are the x-intercepts of the graph.
The y-intercept is found by setting x = 0.
Factorised and completed square forms reveal different features of the same graph.
Common mistakes
Plotting roots correctly but drawing the curve with the wrong orientation.
Confusing x-intercepts and y-intercepts.
Not recognising repeated roots as touching the x-axis.
Drawing straight lines between points instead of a smooth parabola.
Teaching notes
Ask students what each form of the quadratic tells them before sketching.
Use quick feature-finding routines: orientation, roots, y-intercept, turning point.
Compare two similar quadratics and ask what changes on the graph.
Starter ideas
What does y = (x - 2)(x + 5) tell you immediately?
Where does y = x² - 4x + 3 cross the y-axis?
How would the graph of y = -x² differ from y = x²?
Worksheet generation
The worksheet generator can create support content, prior knowledge, worked examples, fluency practice, problem solving, exam-style questions and answers. This link opens the generator directly on this topic.
Open GCSE worksheet generator