Question

Draw the graph of y = x² + 3x – 4 and hence use it to solve x² + 3x – 4 = 0

Answer 1

Let y = x² + 3x – 4

(i) Draw the graph of y = x² + 3x – 4

x	– 5	– 4	– 3	– 2	– 1	0	1	2	3	4
x2	25	16	9	4	1	0	1	4	9	16
3x	–15	– 12	– 9	– 6	– 3	0	3	6	9	12
– 4	– 4	– 4	– 4	– 4	– 4	– 4	– 4	– 4	– 4	– 4
y	6	0	– 4	– 6	– 6	– 4	0	6	14	24

(ii) Plot the points (– 5, 6), (– 4, 0), (– 3, – 4), (– 2, – 6), (– 1, – 6), (0, – 4), (1, 0), (2, 6), (3, 14) on the graph using suitable scale.

(iii) Join the points by a free hand smooth curve.

The smooth curve is the graph of y = x² – 4x + 4

(iv) To solve x + 3x – 4 = 0, subtract x² + 3x – 4 = 0 from y = x² + 3x – 4.

y = 0

∴ The point of intersection with the x-axis is the solution set.

The solution set is – 4 and 1.