SPM 2021 Add Maths Paper 2, Question 4Quadratic Functions

Solved on video in English and Bahasa Melayu · Form 4, Quadratic Functions · 5:26 video

The question

(a)

Diagram 2 shows the curves of quadratic functions f(x) and g(x) which intersect the x-axis at the same two points. The curve f(x) = (x − 3)² + k is an upward parabola whose y-intercept is at 5, and g(x) = −3x² + (m − 4)x − 15 is a downward parabola. Find (a) the value of k.

(b)

Diagram 2 shows the curves f(x) = (x − 3)² + k and g(x) = −3x² + (m − 4)x − 15, which intersect the x-axis at the same two points (with k = −4 from part (a)). (b)(i) Find the value of m. (b)(ii) Hence, find the coordinates of the maximum point of g(x) by using the method of completing the square.

SPM 2021 Add Maths Paper 2, Question 4: the question as drawn in Eduly's video5:26

Part (a)

Step 1

The curve f(x) = (x − 3)² + k cuts the y-axis at (0, 5).

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

Final answer

k = −4

Where students lose marks

Watch out: 9 + k = 5 gives k = 5 − 9 = −4, not 4. Check the sign when solving.

Part (b)

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

Final answer

m = 22; maximum point (3, 12)

Where students lose marks

Watch out: keep both minus signs in −b/a (m = 22, not −14), and after completing the square, state the maximum point.

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