1MA0 Higher June 2013 Paper 1 Q25
25 The expression \(x^2 - 8x + 21\) can be written in the form \((x - a)^2 + b\) for all values of \(x\).
(a) Find the value of \(a\) and the value of \(b\). (3)
The equation of a curve is \(y = \mathrm{f}(x)\) where \(\mathrm{f}(x) = x^2 - 8x + 21\)
The diagram shows part of a sketch of the graph of \(y = \mathrm{f}(x)\).
The minimum point of the curve is \(M\).
(b) Write down the coordinates of \(M\). (1)
| Answer | Mark | Notes |
|---|---|---|
| \(a = 4\), \(b = 5\) | 3 | M1 for sight of \((x - 4)^2\) M1 for \((x - 4)^2 - 16 + 21\) A1 for \(a = 4\), \(b = 5\) OR M1 for \(x^2 - 2ax + a^2 + b\) M1 for \(-2a = -8\) and \(a^2 + b = 21\) A1 for \(a = 4\), \(b = 5\) |
| Answer | Mark | Notes |
|---|---|---|
| (4, 5) | 1 | B1 ft |