Melaka Trial 2025 Add Maths Paper 2, Question 2Quadratic Functions

Solved on video in English · Form 4, Quadratic Functions · 4:35 video

The question

(a)

Diagram 1 shows the cross-section of a semi-circular concrete seat. It is given that h(x) = −2x² + 19x − 42 represents the curve of the outer part of the concrete seat, with A and B the two end points of the base.

(a) Find the distance AB of the seat.

(b)

Diagram 1 shows the cross-section of a semi-circular concrete seat, with h(x) = −2x² + 19x − 42 representing the outer curve and A, B the end points of the base.

(b) By using the method of completing the square, find the maximum distance of the outside of the curve from AB.

Melaka Trial 2025 Add Maths Paper 2, Question 2: the question as drawn in Eduly's video4:35

Part (a)

Step 1

A and B are where the outer curve meets the base, i.e. where h(x) = 0.

Why this step

A and B sit on the base, where the height is zero. So their x-positions are the roots of h(x) = 0.

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

Final answer

AB = 2.5

Where students lose marks

Watch out: AB is the difference of the two roots, so subtract them. Don't give both x-values or use the vertex.

Part (b)

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

Final answer

Maximum distance = 25/8 = 3.125

Where students lose marks

Watch out: when you multiply −2 back in, the −(19/4)² term becomes +361/8. The maximum is the constant 25/8, not 19/4.

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