EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Exam Practice: Using quadratic graphs
Using quadratic graphs · Equations and graphs · Lesson 4 of 6 · 14 marks · 30 minutes
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Instructions
• Answer all the questions.
• Write your answers in the spaces provided.
• The marks for each question are shown in brackets - use this as a guide to how much to write.
• The answers are on separate pages at the back. Attempt every question before you look at them.
• Answer all questions. Show your working.
Question 1 USE THE GRAPH (3 marks)
The graph of y = x² − 2x − 3 is drawn on the grid. (a) Use the graph to solve x² − 2x − 3 = 0. (b) Write down the coordinates of the turning point.
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(Total for Question 1 = 3 marks)
Question 2 USE THE GRAPH (2 marks)
Use the same graph to find estimates for the solutions of x² − 2x − 3 = 2.
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(Total for Question 2 = 2 marks)
Question 3 COMPLETE THE TABLE (2 marks)
Complete the table of values for y = x² − 2x − 3 for x = −2, −1, 0, 1, 2, 3, 4.
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(Total for Question 3 = 2 marks)
Question 4 WRITE DOWN (2 marks)
y = (x − 1)² − 4. Write down the coordinates of the turning point of the graph and the equation of its line of symmetry.
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(Total for Question 4 = 2 marks)
Question 5 SKETCH (3 marks)
Sketch the graph of y = x² − 4, showing where it crosses the axes.
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(Total for Question 5 = 3 marks)
Question 6 EXPLAIN (2 marks)
A quadratic graph has roots at x = 2 and x = 6. Write down the equation of its line of symmetry and explain how you know.
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(Total for Question 6 = 2 marks)
TOTAL FOR PAPER = 14 MARKS
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Answers and mark scheme
Check your answer only once you have written one.
Question 1 (3 marks)
(a) x = −1 and x = 3. (b) (1, −4).
• −1 B1
• 3 B1
• (1, −4) B1
Question 2 (2 marks)
Draw y = 2. The solutions are x ≈ −1.4 and x ≈ 3.4. Accept −1.6 to −1.3 and 3.3 to 3.6.
• Draws y = 2 M1
• Both estimates A1
Question 3 (2 marks)
y = 5, 0, −3, −4, −3, 0, 5
• At least 4 correct M1
• All correct A1
Question 4 (2 marks)
Turning point (1, −4); line of symmetry x = 1.
• (1, −4) B1
• x = 1 B1
Question 5 (3 marks)
A U-shaped parabola with its minimum at (0, −4), crossing the x-axis at (−2, 0) and (2, 0), and the y-axis at (0, −4).
• Correct U shape B1
• x-intercepts ± 2 B1
• y-intercept −4 B1
Question 6 (2 marks)
x = 4; it is halfway between the roots.
• x = 4 B1
• Halfway between the roots C1