WAEC 2018 · Paper 2 · Q11

(a)
Copy and complete the table of values for $y = 2x^2 + x - 10$ for $-5 \le x \le 4$ .

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

$y$ $5$ $-9$ $-10$ $0$

Model answer

$x$ −5 −4 −3 −2 −1 0 1 2 3 4

$y$ 35 18 5 −4 −9 −10 −7 0 11 26

For example, at $x = -5$ : $y = 2(25) - 5 - 10 = 35$ .
(b)
Using scales of 2 cm to 1 unit on the $x$ -axis and 2 cm to 5 units on the $y$ -axis, draw the graph of $y = 2x^2 + x - 10$ for $-5 \le x \le 4$ .
Model answer
Plot every point from the table, then join them with one smooth curve (not straight lines between points).

For (c): (i) $2x^2 + x = 10$ is $y = 0$ : the roots are $x = -2.5$ and $x = 2$ . (ii) $2x^2 + x - 10 = 2x$ : draw the line $y = 2x$ ; it meets the curve at $(-2, -4)$ and $(2.5, 5)$ , so $x = -2$ or $x = 2.5$ .
(c)
Use the graph to find the solution of: (i) $2x^2 + x = 10$ ; (ii) $2x^2 + x - 10 = 2x$ .
Show the answer
(i) $x = -2.5$ or $2$ ; (ii) $x = -2$ or $2.5$

$x$	−5	−4	−3	−2	−1	0	1	2	3	4
$y$	35	18	5	−4	−9	−10	−7	0	11	26

The curve and the line y = 2x.

Worked solution (try it first)

With 2 cm to 1 unit across and 2 cm to 5 units up, plot the ten points and join them with a smooth U-shaped curve.

$2x^2 + x - 10 = 2x$ means the curve meets the line $y = 2x$ .
Draw the line through $(-3, -6)$ , $(0, 0)$ and $(3, 6)$ .
It meets the curve at $x = -2$ and $x = 2.5$ .
(As a check, the equation is $2x^2 - x - 10 = 0$ , which factorises as $(x + 2)(2x - 5) = 0$ .)