Selangor Trial 2025 Add Maths Paper 2, Question 4Quadratic Functions

Solved on video in English · Form 4, Quadratic Functions · 6:31 video

The question

(a)(i)

(a) Diagram 1 shows the graph of the function y = −3(x − h)² + k. (i) Sketch the graph of the function y₁, in Diagram 1, such that the function y₁ is formed by reflecting the graph y = −3(x − h)² + k in the y-axis.

(a)(ii)

(a)(ii) State the function of y₁ in terms of x, h and k.

(b)(i)

(b) Diagram 2 shows the fireworks launching site from a house. The function h(x) = −2x² + 26x − 17 represents the height of the fireworks, where x represents the horizontal distance, in metres, between the house's wall OA and the fireworks. The fireworks explode at the highest point. (i) Determine the horizontal distance of the fireworks from the house's wall OA when the fireworks explode.

(b)(ii)

(b)(ii) State the height, in m, of the fireworks when it explodes.

(b)(iii)

(b)(iii) Find the distance, in m, between the house's wall OA and the point where the firework falls back to the ground.

Selangor Trial 2025 Add Maths Paper 2, Question 4: the question as drawn in Eduly's video6:31

Part (a)(i)

Step 1

A reflection in the y-axis maps every point (x, y) to (−x, y), so the original vertex at (h, k) moves to (−h, k).

Why this step

The y-axis is the mirror, so left and right swap: only x changes sign. Changing y instead is a reflection in the x-axis, a common slip.

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

Final answer

Sketch (see video)

Where students lose marks

Watch out: mirror left to right in the y-axis, not the x-axis, so the vertex lands at (−h, k), still opening downward.

Part (a)(ii)

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

Final answer

y₁ = −3(x + h)² + k

Where students lose marks

Watch out: a y-axis reflection replaces x with −x. Flipping the whole function to +3(x − h)² − k is an x-axis reflection.

Part (b)(i)

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

Final answer

x = 13/2 (6.5 m)

Where students lose marks

Watch out: use x = −b/(2a) with a = −2 and keep the signs straight: −26/−4 is positive 6.5, not −6.5.

Part (b)(ii)

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

Final answer

135/2 (67.5 m)

Where students lose marks

Watch out: height is the y-value, so substitute x = 13/2 into h(x). Don't repeat 6.5, and take care squaring 13/2.

Part (b)(iii)

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

Final answer

12.31 m

Where students lose marks

Watch out: 4(−2)(−17) = +136, so the discriminant is 676 − 136 = 540. Choose the far root 12.31, not 0.69.

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