4MA1/2F Jun 2023, Question 20: Quadratic Graphs and the Parabola

Part (a) · 2 marks

Fill in the missing y values in the table for y = x² – x – 4 using x = –3, –1, 0, 2 and 3.

1. 1Substitute each x into x² − x − 4
2. 2x = −3: 9 + 3 − 4 = 8; x = −1: 1 + 1 − 4 = −2; x = 0: −4
3. 3x = 2: 4 − 2 − 4 = −2; x = 3: 9 − 3 − 4 = 2
4. 48, 2, −2, −4, −4, −2, 2

Answer8, 2, −2, −4, −4, −2, 2

Part (b) · 2 marks

Draw the curve y = x² – x – 4 on the grid, using x values from –3 to 3.

1. 1Plot the points from the table: (−3,8), (−2,2), (−1,−2), (0,−4), (1,−4), (2,−2), (3,2)
2. 2Join the points with a smooth curve, ensuring it passes through all points and curves between (0,−4) and (1,−4)

AnswerA smooth curve through (−3, 8), (−2, 2), (−1, −2), (0, −4), (1, −4), (2, −2) and (3, 2), curving between (0, −4) and (1, −4)

More past-paper questions on quadratic graphs and the parabola

• 4MA1/1HR Jan 2022 Q4 · 4 marks
• 4MA1/2HR Jan 2020 Q15 · 4 marks
• 4MA1/1H Jan 2019 Q6 · 6 marks
• 4MA1/2HR Jan 2019 Q20 · 4 marks
• 4MA1/1F Jun 2019 Q18 · 4 marks
• 4MA1/2FR Jun 2019 Q19 · 4 marks