GraphsKey Facts

Key Features of Quadratic Graphs

Part of Quadratic Graphs · GCSE GCSE Mathematics revision

This key facts covers Key Features of 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 4 of 10 in this topic. Use this key facts to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 4 of 10

Practice

14 questions

Recall

12 flashcards

Key Features of Quadratic Graphs

Vertex (Turning Point)

  • For y = ax² + bx + c: x-coordinate = -b/(2a)
  • Substitute back to find y-coordinate
  • Minimum when a > 0, Maximum when a < 0

Y-intercept

  • Set x = 0: y = c
  • Always at point (0, c)

X-intercepts (Roots)

  • Set y = 0: Solve ax² + bx + c = 0
  • Methods: Factoring, quadratic formula, completing the square
  • Can have: 2 roots, 1 root (repeated), or no real roots

Axis of Symmetry

  • Vertical line: x = -b/(2a)
  • Passes through vertex
  • Parabola is symmetric about this line

Keep building this topic

Read this section alongside the surrounding pages in Quadratic Graphs. That gives you the full topic sequence instead of a single isolated revision point.

Practice Questions for Quadratic Graphs

The quadratic y = -3x² + 2x - 1 has a negative coefficient of x². What shape does this parabola make?

  • A. U-shape (opens upward, minimum point)
  • B. ∪-shape (opens upward, minimum point at top)
  • C. ∩-shape (opens downward, maximum point)
  • D. S-shape (neither minimum nor maximum)
1 markfoundation

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.

2 marksstandard

Quick Recall Flashcards

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)
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)

14 questions on Quadratic Graphs — practise free

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