| Date | May 2013 | Marks available | 2 | Reference code | 13M.1.sl.TZ1.9 |
| Level | SL only | Paper | 1 | Time zone | TZ1 |
| Command term | Find | Question number | 9 | Adapted from | N/A |
Question
The graph of the quadratic function \(f (x) = c + bx − x^2\) intersects the y-axis at point A(0, 5) and has its vertex at point B(2, 9).
Write down the value of c.
Find the value of b.
Find the x-intercepts of the graph of f .
Write down \(f (x)\) in the form \(f (x) = −(x − p) (x + q)\).
Markscheme
5 (A1) (C1)
\(\frac{{ - b}}{{2( - 1)}} = 2\) (M1)
Note: Award (M1) for correct substitution in axis of symmetry formula.
OR
\(y = 5 + bx - x^2\)
\(9 = 5 + b (2) - (2)^2\) (M1)
Note: Award (M1) for correct substitution of 9 and 2 into their quadratic equation.
\((b =) 4\) (A1)(ft) (C2)
Note: Follow through from part (a).
5, −1 (A1)(ft)(A1)(ft) (C2)
Notes: Follow through from parts (a) and (b), irrespective of working shown.
\(f (x) = -(x - 5)(x + 1)\) (A1)(ft) (C1)
Notes: Follow through from part (c).
Examiners report
Many candidates did not see the connection between the x-intercepts and the factored form of a quadratic function. The syllabus explicitly sates that the graphs of quadratics should be linked to solutions of quadratic equations by factorizing and vice versa. This was one of the most challenging questions for candidates.
Many candidates did not see the connection between the x-intercepts and the factored form of a quadratic function. The syllabus explicitly sates that the graphs of quadratics should be linked to solutions of quadratic equations by factorizing and vice versa. This was one of the most challenging questions for candidates.
Many candidates did not see the connection between the x-intercepts and the factored form of a quadratic function. The syllabus explicitly sates that the graphs of quadratics should be linked to solutions of quadratic equations by factorizing and vice versa. This was one of the most challenging questions for candidates.
Many candidates did not see the connection between the x-intercepts and the factored form of a quadratic function. The syllabus explicitly sates that the graphs of quadratics should be linked to solutions of quadratic equations by factorizing and vice versa. This was one of the most challenging questions for candidates.
