WAEC 2020 · Paper 2 · Q7

(a)
Copy and complete the table of values for the relation $y = 2x^2 - 5x - 3$ for $-3 \le x \le 5$ .

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

$y$ $30$ $-3$ $9$

Model answer

$x$ −3 −2 −1 0 1 2 3 4 5

$y$ 30 15 4 −3 −6 −5 0 9 22

For example, at $x = -2$ : $y = 2(4) + 10 - 3 = 15$ .
(b)
Using a scale of 2 cm to 1 unit on the $x$ -axis and 2 cm to 5 units on the $y$ -axis, draw the graph of $y = 2x^2 - 5x - 3$ for $-3 \le x \le 5$ .
Model answer
Plot every point from the table, then join them with one smooth curve (not straight lines between points).

For (c): (i) $2x^2 - 4x - 7 = x - 4$ simplifies to $2x^2 - 5x - 3 = 0$ , which is $y = 0$ : $x = -0.5$ or $x = 3$ . (ii) The line of symmetry is halfway between the roots: $x = 1.25$ . (iii) Draw $y = 7$ : $x \approx −1.3 and 3.8$ .
(c)(i)
Using the graph, find the truth set of $2x^2 - 4x - 7 = x - 4$ .
Separate values with commas, e.g. 3, −2
(c)(ii)
Determine the equation of the line of symmetry.
(c)(iii)
Find the values of $x$ for which $y = 7$ .
Separate values with commas, e.g. 3, −2

$x$	−3	−2	−1	0	1	2	3	4	5
$y$	30	15	4	−3	−6	−5	0	9	22

The curve, its line of symmetry, and y = 7.

Worked solution (try it first)

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

Take $x - 4$ from both sides of $2x^2 - 4x - 7 = x - 4$ : $2x^2 - 5x - 3 = 0$ , which is $y = 0$ .
The curve crosses the $x$ -axis at $x = -0.5$ and $x = 3$ , so the truth set is $\{-0.5, 3\}$ .

The line of symmetry is halfway between the roots: $x = \frac{-0.5 + 3}{2} = 1.25$ .
Its equation is $x = 1.25$ .