EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Exam Practice: Quadratic Graphs
Quadratic graphs · Graphs · Lesson 6 of 8 · 11 marks · 20 minutes
Name Date
Answer all questions. Show your working. All questions are non-calculator.
Question 1 NON-CALCULATOR [2 marks]
Complete the table of values for y = x² − 3x + 1 for x = −1, 0, 1, 2, 3, 4.
Question 2 NON-CALCULATOR [5 marks]
The graph of y = x² − 2x − 3 is drawn for values of x from −2 to 4. (a) Write down the roots of x² − 2x − 3 = 0. (b) Write down the coordinates of the turning point. (c) Write down the equation of the line of symmetry. (d) Use the graph to find estimates for the solutions of x² − 2x − 3 = 2.
Question 3 NON-CALCULATOR [2 marks]
The graph of a quadratic crosses the x-axis at x = −2 and x = 6. Write down the equation of its line of symmetry, and explain how you know.
Question 4 NON-CALCULATOR [2 marks]
Sam says the graph of y = x² + 4 crosses the x-axis twice. Is Sam right? Explain your answer.
Answers
Check your answer only once you have written one.
Question 1 [2 marks]
y = 5, 1, −1, −1, 1, 5
▸ At least 4 correct values B1
▸ All 6 correct B1
Question 2 [5 marks]
(a) x = −1 and x = 3 (b) (1, −4) (c) x = 1 (d) Draw y = 2: x ≈ −1.4 and x ≈ 3.4
▸ (a) −1 and 3 B1
▸ (b) (1, −4) B1
▸ (c) x = 1 B1
▸ (d) Line y = 2 drawn, or reading at y = 2 M1
▸ (d) −1.4 to −1.5 and 3.4 to 3.5 A1
Question 3 [2 marks]
x = 2. The line of symmetry is halfway between the roots: (−2 + 6)/2 = 2.
▸ x = 2 B1
▸ Halfway between the roots C1
Question 4 [2 marks]
No. x² is never negative, so x² + 4 is always at least 4. The graph never reaches y = 0.
▸ No B1
▸ A reason, e.g. the minimum value is 4, or x² ≥ 0 C1