WAEC 2017 · Paper 2 · Q7

(a)
Copy and complete the table of values for $y = 2x^2 - 7x - 9$ for $-3 \le x \le 6$ .

$x$ $-3$ $-2$ $-1$ $0$ $1$ $2$ $3$ $4$ $5$ $6$

$y$ $13$ $-9$ $-14$ $-12$ $6$

Model answer

$x$ $-3$ $-2$ $-1$ $0$ $1$ $2$ $3$ $4$ $5$ $6$

$y$ $30$ $13$ $0$ $-9$ $-14$ $-15$ $-12$ $-5$ $6$ $21$

For example $x = -3$ : $18 + 21 - 9 = 30$ , and $x = 2$ : $8 - 14 - 9 = -15$ .
(b)
Using scales of 2 cm to 1 unit on the $x$ -axis and 2 cm to 4 units on the $y$ -axis, draw the graph of $y = 2x^2 - 7x - 9$ for $-3 \le x \le 6$ .
Model answer
Plot every point from the table, then join them with one smooth curve (not straight lines between points). Scale: 2 cm to 1 unit across, 2 cm to 4 units up.

For (c): (i) $2x^2 - 7x = 26$ is $2x^2 - 7x - 9 = 17$ , so draw $y = 17$ : $x \approx −2.3 and 5.8$ . (ii) The minimum point is about $(1.75, -15.1)$ . (iii) $2x^2 - 7x < 9$ means $y < 0$ : the curve is below the $x$ -axis for $-1 < x < 4.5$ .
(c)
Use the graph to estimate the: (i) roots of the equation $2x^2 - 7x = 26$ ; (ii) coordinates of the minimum point of $y$ ; (iii) range of values for which $2x^2 - 7x < 9$ .
Separate values with commas, e.g. 3, −2

$x$	$-3$	$-2$	$-1$	$0$	$1$	$2$	$3$	$4$	$5$	$6$
$y$		$13$		$-9$	$-14$		$-12$		$6$

$x$	$-3$	$-2$	$-1$	$0$	$1$	$2$	$3$	$4$	$5$	$6$
$y$	$30$	$13$	$0$	$-9$	$-14$	$-15$	$-12$	$-5$	$6$	$21$

The curve with the line y = 17.

Worked solution (try it first)

Plot the ten points with the given scales and join them with a smooth U-shaped curve.

Make the equation match the curve: $2x^2 - 7x = 26$ is $2x^2 - 7x - 9 = 17$ , that is $y = 17$ .
Draw the line $y = 17$ and read where it meets the curve: $x \approx -2.3$ and $x \approx 5.8$ .

$2x^2 - 7x < 9$ is $2x^2 - 7x - 9 < 0$ , that is $y < 0$ : where the curve is below the $x$ -axis.
It crosses the axis at $x = -1$ and $x = 4.5$ , so $-1 < x < 4.5$ .