SPM 2024 Add Maths Paper 2, Question 2Quadratic Functions
Solved on video in English and Bahasa Melayu · Form 4, Quadratic Functions · 5:11 video
The question
The quadratic function f(x) = 3x² + 3px + p, such that p is a constant, has a minimum value of −1.
(a) Using the method of completing the square, find the values of p.
(b) Sketch the graph of f(x) using the largest value of p from (a).
Step 1
Factor out 3 from the x-terms: f(x) = 3[x² + px + p/3]
Why this step
Completing the square needs the x² term to have coefficient 1, so we take 3 out first. That is why the lone p becomes p/3 inside the bracket.
18 more steps, each with the reason for it, in the full solution
Final answer
p = 2 or p = −2/3; Upward parabola: minimum point (−1, −1), axis of symmetry x = −1, y-intercept (0, 2), x-intercepts at x = −1 ± 1/√3 (i.e., x ≈ −0.423 and x ≈ −1.577)
Where students lose marks
Watch the sign of the constant when reading the minimum, and label every feature on your sketch: vertex, axis, y-intercept, both x-intercepts.
Watch every step of this question solved on video (5:11), with the reason behind each step and a box that checks your own answer.
No card. Every past-year question on video, in English and BM.
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