| Date | May 2011 | Marks available | 4 | Reference code | 11M.1.hl.TZ2.1 |
| Level | HL only | Paper | 1 | Time zone | TZ2 |
| Command term | Find | Question number | 1 | Adapted from | N/A |
Question
The quadratic function f(x)=p+qx−x2 has a maximum value of 5 when x = 3.
Find the value of p and the value of q .
The graph of f(x) is translated 3 units in the positive direction parallel to the x-axis. Determine the equation of the new graph.
Markscheme
METHOD 1
f′(x)=q−2x=0 M1
f′(3)=q−6=0
q = 6 A1
f(3) = p + 18 − 9 = 5 M1
p = −4 A1
METHOD 2
f(x)=−(x−3)2+5 M1A1
=−x2+6x−4
q = 6, p = −4 A1A1
[4 marks]
g(x)=−4+6(x−3)−(x−3)2 (=−31+12x−x2) M1A1
Note: Accept any alternative form which is correct.
Award M1A0 for a substitution of (x + 3) .
[2 marks]
Examiners report
In general candidates handled this question well although a number equated the derivative to the function value rather than zero. Most recognised the shift in the second part although a number shifted only the squared value and not both x values.
In general candidates handled this question well although a number equated the derivative to the function value rather than zero. Most recognised the shift in the second part although a number shifted only the squared value and not both x values.
