The answer
(a) \(-7 + (x - 4)^2\)
(b) \((4, -7)\)
O-Level E-Math 2016 Paper 1 Question 11 · Verified worked solution by the Genius Plus Academy teaching team
The question
(a) Express \(9 - 8x + x^2\) in the form \(p + (x + q)^2\). [2]
(b) Write down the coordinates of the minimum point of the graph of \(y = 9 - 8x + x^2\). [1]
(a) Write in descending powers and complete the square: \(x^2 - 8x + 9 = (x - 4)^2 - 16 + 9 = (x - 4)^2 - 7 = -7 + (x - 4)^2\). So \(p = -7\) and \(q = -4\).
(b) The graph \(y = (x-4)^2 - 7\) is an upward parabola; its minimum occurs where the bracket is zero, at \(x = 4\), giving \(y = -7\). Minimum point \((4, -7)\).
Answer: (a) \(-7 + (x - 4)^2\)
(b) \((4, -7)\)
Same structure, different numbers
Swap the constants, dress a quadratic as a length, hide a derivative inside an integral, and a student sees a brand new problem. The structure underneath is the same, and so is the method. Once a student can name the structure, a whole row of questions that look different start to open the same way.
That is where marks really leak: in choosing the method, not in the algebra that follows. We call it Lock and Key, name the lock, then the key follows.
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Same skill, different papers. Each has a verified worked solution.
Genius Plus Academy · O-Level & IP Mathematics
Our O-Level E-Math tuition trains the same recognise-the-structure method these worked solutions show, taught by a team that has marked these papers for years. It runs within our weekly Secondary Math programme, Sec 1 to 4 and IP.
It is a completing the square question from Functions & graphs (quadratics), worth 3 marks: 2 + 1.
Yes. IP (Integrated Programme) schools teach the same O-Level Mathematics content; they just sequence it differently and set their own internal exams, so these worked solutions apply to IP students too.
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