SPM 2023 Add Maths Paper 2, Question 5Quadratic Functions

Solved on video in English and Bahasa Melayu · Form 4, Quadratic Functions · 6:12 video

The question

(a)

It is given that (2x + 3) is one of the factors of f(x) = x(5 − 2x) + m, where m is a constant.

(a) Find the value of m.

(b)

It is given that (2x + 3) is one of the factors of f(x) = x(5 − 2x) + m, and m = 12.

(b) Using the method of completing the square, express f(x) in the form f(x) = a(x − h)² + k, where a, h and k are constants. Hence, sketch the graph of f(x) for 0 ≤ x ≤ 4.

(c)

Using a = −2, h = 5/4 and k = 121/8 from part (b):

(c) Using the same axes as in (b), sketch and label the graph of g(x) = (a − 1)(x − h)² + k.

SPM 2023 Add Maths Paper 2, Question 5: the question as drawn in Eduly's video6:12

Part (a)

Step 1

Expand: f(x) = x(5 − 2x) + m = 5x − 2x² + m = −2x² + 5x + m.

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

Final answer

m = 12

Where students lose marks

Watch out: the root of (2x + 3) is x = −3/2. Square the negative fraction carefully; sign slips ruin m.

Part (b)

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

Final answer

f(x) = −2(x − 5/4)² + 121/8; max (5/4, 121/8), curve from (0, 12) to (4, 0)

Where students lose marks

Take −2 out of the x-terms carefully, and remember it multiplies −25/16 too. Label the maximum point and both endpoints on your sketch.

Part (c)

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

Final answer

g(x) = −3(x − 5/4)² + 121/8; sketch: same maximum, narrower than f

Where students lose marks

Watch out: g shares f's maximum but is narrower. Sketch it on the same axes, inside f, and label both curves.

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