SPM 2018 Add Maths Paper 1, Question 18Quadratic Functions

Solved on video in English and Bahasa Melayu · 3 marks · Form 4, Quadratic Functions · 3:58 video

The question

Diagram 8 shows the graph y = a(x-p)² + q, where a, p and q are constants. The straight line y = -8 is the tangent to the curve at point H. (a) State the coordinates of H. (b) Find the value of a.

[3 marks]

SPM 2018 Add Maths Paper 1, Question 18: the question as drawn in Eduly's video3:58

Step 1

Since y = -8 is the tangent to the curve at H and the parabola opens upward, H must be the vertex (minimum point) of the curve, i.e. H = (p, q) with q = -8.

Why this step

A flat tangent on an upward bowl can only touch its lowest point. So H is the vertex, and the tangent's height gives q straight away.

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

Final answer

H = (3, −8); a = 1/2

Where students lose marks

Watch out: the tangent y = −8 gives q directly, and a needs an x-intercept like (7, 0), not the vertex.

Watch every step of this question solved on video (3:58), with the reason behind each step and a box that checks your own answer.

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