AQA•GCSE•Mathematics•Algebra
Quadratic graphs
AQA GCSE Mathematics practice questions with step-by-step solutions
Start Practicing Now
Generate unlimited Quadratic graphs questions. Choose your difficulty level, get instant feedback, and master this topic.
Unlimited questionsDetailed solutionsAQA exam style
Sample Questions
Try before you startPreview AQA GCSE style questions on Quadratic graphs. Click "Show Solution" to see the step-by-step answer.
EasyQuestion 1
[2 marks]The graph of y = x² - 4 is shown.
(a) Write down the y-intercept of the graph.
(b) Write down the coordinates of the minimum point.
Solution for Question 1
MediumQuestion 2
[4 marks]Complete the table of values for y = x² - 2x - 3
| x | -2 | -1 | 0 | 1 | 2 | 3 | 4 |
|---|----|----|---|---|---|---|---|
| y | | | | | | | |
Use your table to draw the graph of y = x² - 2x - 3.
Solution for Question 2
HardQuestion 3
[5 marks]The graph shows y = x² - 2x - 3.
(a) Write down the roots of the equation x² - 2x - 3 = 0.
(b) Write down the equation of the line of symmetry.
(c) Find the coordinates of the minimum point.
(d) Use the graph to solve x² - 2x - 3 = 5.
Solution for Question 3
Want more questions like these?
Generate Unlimited QuestionsAbout Quadratic graphs in AQA GCSE
Quadratic graphs are U-shaped curves called parabolas. They are formed when you plot a quadratic function of the form y = ax² + bx + c.
**Key Features of Quadratic Graphs:**
**Shape:**
- If a > 0 (positive x²): U-shaped (minimum point)
- If a < 0 (negative x²): n-shaped (maximum point)
**Key Points:**
- **Vertex (turning point):** The highest or lowest point
- **Y-intercept:** Where the graph crosses the y-axis (when x = 0) - this equals c
- **X-intercepts (roots):** Where the graph crosses the x-axis (when y = 0)
- **Line of symmetry:** Vertical line through the vertex
**Plotting Quadratic Graphs:**
1. Create a table of values for x and y
2. Choose x values either side of the vertex
3. Calculate y for each x value
4. Plot the points and draw a smooth curve
5. Label key features
**Finding the Vertex:**
For y = ax² + bx + c, the x-coordinate of the vertex is x = -b/(2a)
**From a Graph:**
- Read off roots from x-intercepts
- Read off minimum/maximum from vertex
- Identify line of symmetry
**Exam Tips:**
- Use a smooth curve, not straight lines between points
- Include enough points to show the shape clearly
- Always label axes and key features
What you'll practice
Exam-style questions matching the AQA specification, from basic to challenging
How it works
AI generates unique questions each time, with full worked solutions and mark schemes