Knowledge Organiser: Quadratic Graphs
This topic summary covers Knowledge Organiser: 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 10 of 10 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.
Topic position
Section 10 of 10
Practice
14 questions
Recall
12 flashcards
Knowledge Organiser: Quadratic Graphs
Key Terms
- Parabola: The U-shaped (or ∩-shaped) curve of a quadratic graph
- Vertex: The turning point of the parabola — minimum or maximum
- Axis of symmetry: The vertical line x = −b ÷ (2a) through the vertex
- Roots: The x-intercepts where the curve crosses the x-axis (y = 0)
- y-intercept: Where the curve crosses the y-axis; equals c in y = ax² + bx + c
- Coefficient a: Determines whether the parabola opens up (a > 0) or down (a < 0)
Must-Know Facts
- If a > 0, the parabola is U-shaped with a minimum point
- If a < 0, the parabola is ∩-shaped with a maximum point
- The y-intercept is always at (0, c)
- The parabola is symmetric about its axis of symmetry
- Always join plotted points with a smooth curve — never straight lines
- A quadratic can have 0, 1, or 2 roots depending on where the curve meets the x-axis
Key Formulas
- General form: y = ax² + bx + c
- x-coordinate of vertex: x = −b ÷ (2a)
- y-intercept: set x = 0, giving y = c
- Roots: set y = 0, solve ax² + bx + c = 0 (by factorising or the quadratic formula)
- Axis of symmetry: x = −b ÷ (2a)
Common Mistakes
- U-shape vs ∩-shape: Positive a → U-shaped (minimum); negative a → ∩-shaped (maximum) — check the sign of a first
- y-intercept ≠ vertex: The y-intercept is at (0, c); the vertex is at x = −b/(2a) — these are different points
- Plotting without enough points: Calculate at least 5-7 points and join with a smooth curve — never straight lines between points
- Reading roots from graph: Roots (solutions) are where the curve crosses the x-axis, not the y-axis
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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
14 questions on Quadratic Graphs — practise free
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