| Date | May 2017 | Marks available | 4 | Reference code | 17M.1.sl.TZ1.15 |
| Level | SL only | Paper | 1 | Time zone | TZ1 |
| Command term | Find | Question number | 15 | Adapted from | N/A |
Question
The graph of a quadratic function has \(y\)-intercept 10 and one of its \(x\)-intercepts is 1.
The \(x\)-coordinate of the vertex of the graph is 3.
The equation of the quadratic function is in the form \(y = a{x^2} + bx + c\).
Write down the value of \(c\).
Find the value of \(a\) and of \(b\).
Write down the second \(x\)-intercept of the function.
Markscheme
10 (A1) (C1)
Note: Accept \((0,{\text{ }}10)\).
[1 mark]
\(3 = \frac{{ - b}}{{2a}}\)
\(0 = a{(1)^2} + b(1) + c\)
\(10 = a{(6)^2} + b(6) + c\)
\(0 = a{(5)^2} + b(5) + c\) (M1)(M1)
Note: Award (M1) for each of the above equations, provided they are not equivalent, up to a maximum of (M1)(M1). Accept equations that substitute their 10 for \(c\).
OR
sketch graph showing given information: intercepts \((1,{\text{ }}0)\) and \((0,{\text{ }}10)\) and line \(x = 3\) (M1)
\(y = a(x - 1)(x - 5)\) (M1)
Note: Award (M1) for \((x - 1)(x - 5)\) seen.
\(a = 2\) (A1)(ft)
\(b = - 12\) (A1)(ft) (C4)
Note: Follow through from part (a).
If it is not clear which is \(a\) and which is \(b\) award at most (A0)(A1)(ft).
[4 marks]
5 (A1) (C1)
[1 mark]
