| 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 \(f(x) = p + qx - {x^2}\) 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
\( = - {x^2} + 6x - 4\)
q = 6, p = −4 A1A1
[4 marks]
\(g(x) = - 4 + 6(x - 3) - {(x - 3)^2}{\text{ }}( = - 31 + 12x - {x^2})\) 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.
