This deep dive covers Worked Examples 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 6 of 9 in this topic. Use this deep dive to connect the idea to the wider topic before moving on to questions and flashcards.
Topic position
Section 6 of 9
Practice
14 questions
Recall
12 flashcards
Worked Examples
Example 1: Analyzing y = x² - 6x + 5
Find key features and sketch the graph
Solution:
- Vertex: x = -(-6)/(2×1) = 3, y = 3² - 6(3) + 5 = -4
Vertex: (3, -4) - Y-intercept: Set x = 0: y = 5, Point: (0, 5)
- X-intercepts: x² - 6x + 5 = 0
(x - 1)(x - 5) = 0, so x = 1 or x = 5 - Shape: a = 1 > 0, so opens upward
- Axis of symmetry: x = 3
Example 2: Table of Values for y = -x² + 4x - 3
| x | -x² | +4x | -3 | y |
|---|---|---|---|---|
| 0 | 0 | 0 | -3 | -3 |
| 1 | -1 | 4 | -3 | 0 |
| 2 | -4 | 8 | -3 | 1 |
| 3 | -9 | 12 | -3 | 0 |
| 4 | -16 | 16 | -3 | -3 |
Vertex at (2, 1), opens downward, x-intercepts at 1 and 3