17M.1.SL.TZ1.T_15

pestleMathematicsAISLPaper 117M· sl-2-4-key-features-of-graphs-intersections-using-technologysource ↗

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 $c$ .

[1]

Find the value of $a$ and of $b$ .

[4]

Write down the second $x$ -intercept of the function.

[1]

Markscheme / solution

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

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 $c$ .

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]

Examiners’ report

[N/A]