- Use smooth curves: No sharp corners or straight line segments
- Check the shape: Positive a = smile (∪), negative a = frown (∩)
- Mark key points: Clearly label vertex, intercepts, and any given points
- Use symmetry: If (1, 3) is on the curve and axis is x = 4, then (7, 3) is also on it
- Extend appropriately: Draw curve long enough to show the full parabola shape
- Check by substitution: Verify key points satisfy the equation
This exam tips covers Exam Tips for Quadratic Graphs within Quadratic Graphs for GCSE Mathematics. Revise Quadratic Graphs in Graphs for GCSE Mathematics with 14 exam-style questions and 12 flashcards. This is a high-frequency topic, so it is worth revising until the explanation feels precise and repeatable. It is section 7 of 10 in this topic. Treat this as a marking guide for what examiners are looking for, not just a fact list.
Practice questions for Quadratic Graphs
The quadratic y = -3x² + 2x - 1 has a negative coefficient of x². What shape does this parabola make?
Explain how the sign of the coefficient a in y = ax² + bx + c determines the shape of the parabola. Your answer should refer to both cases: a > 0 and a < 0.
Quick recall flashcards
What is a parabola?
The U-shaped (or n-shaped) curve produced by a quadratic graph.
- a > 0: opens upward (U-shape, minimum)
- a < 0: opens downward (n-shape, maximum)
What are the roots of a quadratic graph?
The x-values where the graph crosses the x-axis (where y = 0).
A quadratic can have:
- 2 roots (crosses x-axis twice)
- 1 root (just touches x-axis)
- 0 roots (entirely above or below x-axis)