Edexcel IALGeneralGeneral Applications6 Marks
Given the function f(x) = x^2 - 6x + 13.
- (a)Express f(x) in the form (x + a)^2 + b, where a and b are integers to be found.[3]
- (b)Hence, or otherwise, write down the minimum value of f(x) and the value of x at which it occurs.[2]
- (c)State the range of f(x).[1]
Mark scheme
Marking points from the official mark scheme. The mark or mark type is shown in brackets.
- "(a)"
- M1 for attempting to complete the square (x - 3)^2 or (x + a)^2, where a is half of the x-coefficient.
- A1 for (x - 3)^2 - 9 + 13 or (x - 3)^2 + 4 (intermediate step or correct b).
- A1 for (x - 3)^2 + 4 (correct final form with a = -3, b = 4).
- "(b)"
- B1 for minimum value = 4 (ft their b from part (a)).
- B1 for value of x = 3 (ft their -a from part (a)).
- "(c)"
- B1 for f(x) ≥ 4 (or y ≥ 4 or [4, ∞)). (ft their minimum value from part (b)).
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