SPM 2020 Add Maths Paper 2, Question 2Quadratic Functions

Solved on video in English and Bahasa Melayu · Form 4, Quadratic Functions · 7:40 video

The question

(a)

The graph of the quadratic function f(x) = x² - 3x - m intersects the x-axis at 2h and 2k, while the quadratic equation mx² + nx - 1 = 0 has roots h and k, where m and n are constants and m > 0. (a) Find the value of m and of n.

(b)(i)

(b)(i) Hence, by using the method of completing the square, find the minimum value of f(x).

(b)(ii)

(b)(ii) Sketch the graph of f(x).

SPM 2020 Add Maths Paper 2, Question 2: the question as drawn in Eduly's video7:40

Part (a)

Step 1

For f(x) = x² - 3x - m, the x-intercepts are the roots 2h and 2k of x² - 3x - m = 0.

Why this step

f cuts the x-axis where f(x) = 0, so 2h and 2k are f's roots. Don't mix them with h and k, which belong to the other equation.

6 more steps, each with the reason for it, in the full solution

Final answer

m = 2, n = −3

Where students lose marks

Watch out: f has roots 2h and 2k, the equation has roots h and k. Use sum and product of roots, not the discriminant.

Part (b)(i)

5 more steps, each with the reason for it, in the full solution

Final answer

Minimum value = −17/4 (at x = 3/2)

Where students lose marks

Watch out: the question asks for the minimum value, −17/4, not the minimum point. Show completing the square, not just −b/(2a).

Part (b)(ii)

6 more steps, each with the reason for it, in the full solution

Final answer

Sketch (see video)

Where students lose marks

Watch out: show a point on each side of the minimum, and draw a smooth parabola, not a pointed or flat curve.

Watch every step of this question solved on video (7:40), with the reason behind each step and a box that checks your own answer.

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