Date | November 2016 | Marks available | 2 | Reference code | 16N.1.SL.TZ0.T_9 |
Level | Standard Level | Paper | Paper 1 (with calculator from previous syllabus) | Time zone | Time zone 0 |
Command term | Find | Question number | T_9 | Adapted from | N/A |
Question
The graph of the quadratic function f(x)=c+bx−x2 intersects the x-axis at the point A(−1, 0) and has its vertex at the point B(3, 16).
Write down the equation of the axis of symmetry for this graph.
Find the value of b.
Write down the range of f(x).
Markscheme
* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.
x=3 (A1)(A1) (C2)
Note: Award (A1) for x= constant, (A1) for the constant being 3.
The answer must be an equation.
[2 marks]
−b2(−1)=3 (M1)
Note: Award (M1) for correct substitution into axis of symmetry formula.
OR
b−2x=0 (M1)
Note: Award (M1) for correctly differentiating and equating to zero.
OR
c+b(−1)−(−1)2=0 (or equivalent)
c+b(3)−(3)2=16 (or equivalent) (M1)
Note: Award (M1) for correct substitution of (−1, 0) and (3, 16) in the original quadratic function.
(b=) 6 (A1)(ft) (C2)
Note: Follow through from part (a).
[2 marks]
(−∞, 16] OR ]−∞, 16] (A1)(A1)
Note: Award (A1) for two correct interval endpoints, (A1) for left endpoint excluded and right endpoint included.
[2 marks]