WMA11/01 Jan 2023, Question 8: Quadratics from Their Turning Point

Part (a) · 2 marks

Find the equation of line l in the form y = mx + c, given it passes through (0, −12) and (4, 0).

1. 1Gradient m = (0 − (−12))/(4 − 0) = 3
2. 2c = −12, so y = 3x − 12

Answery = 3x − 12

Part (b) · 1 mark

Using the symmetry of the quadratic with minimum at (7, −18) and one x-intercept at 4, deduce the other intercept k.

1. 1The minimum is on the line of symmetry x = 7
2. 2The roots are symmetric about x = 7: 4 is 3 to the left, so k = 7 + 3 = 10

Answerk = 10

Part (c) · 3 marks

Find the quadratic expression f(x) for curve C using its minimum point and x-intercepts.

1. 1f(x) = A(x − 4)(x − 10)
2. 2At (7, −18): −18 = A(3)(−3) = −9A, so A = 2
3. 3f(x) = 2(x − 4)(x − 10) = 2x² − 28x + 80

Answerf(x) = 2(x − 4)(x − 10) = 2x² − 28x + 80

Part (d) · 2 marks

Write inequalities in x and y that define the shaded region R bounded by the y-axis, curve C and line l.

1. 1R lies above the line l: y > 3x − 12
2. 2R lies below the curve C: y < 2(x − 4)(x − 10)
3. 3R lies to the right of the y-axis and left of x = 4: 0 < x < 4
4. 4R: 3x − 12 < y < 2(x − 4)(x − 10), 0 < x < 4

Answer3x − 12 < y < 2(x − 4)(x − 10), 0 < x < 4

More past-paper questions on quadratics from their turning point

• WMA11/01 Jan 2024 Q9 · 10 marks
• WMA11/01 Oct 2024 Q4 · 10 marks
• WMA11/01 Jun 2022 Q5 · 9 marks
• WMA11/01 Jan 2021 Q4 · 8 marks
• WMA11/01 Jun 2021 Q5 · 8 marks