MRSM Trial 2025 Add Maths Paper 2, Question 5Quadratic Functions

Johari's jump from a riverbank into the river can be represented by the quadratic function h(t) = −8t² + 32t + 96, where t is the time in seconds and h is the height in cm.

(a)(i) By using the completing the square method, express h(t) in the form p(t − q)² + r, where p, q and r are constants.

For h(t) = −8t² + 32t + 96 = −8(t − 2)² + 128:

(a)(ii) Hence, sketch the graph of h(t).

Johari's jump is represented by h(t) = −8t² + 32t + 96 = −8(t − 2)² + 128 (t in seconds, h the height in cm).

(b) Calculate the total vertical distance, in cm, of Johari's jump from the riverbank until he reaches the water surface.

For the quadratic function written as p(t − q)² + r (from h(t) = −8(t − 2)² + 128):

(c) Determine the effect on the equation of the axis of symmetry if the value of the coefficient p changes to −3.