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
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.
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 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)