2.2 Solving
equations graphically
The solution of the equation f (x) = g (x)
can be solved by graphical method.
Step
1: Draw the graphs of y = f (x) and y = g (x) on the same axes.
Step
2: The points of intersection of the graphs are the
solutions of the equation
f (x) = g
(x). Read the values of x from the graph.
Solution of an Equation by Graphical Method
Example 1:
(d)
Example 1:
(a) The following table shows the corresponding values
of x and y for the equation y
= 2x^{2} – x – 3.
x

–2

–1

–0.5

1

2

3

4

4.5

5

y

7

m

– 2

–2

3

12

n

33

42

Calculate the value of m and n.
(b) For this part of the question, use graph paper. You
may use a flexible curve rule.
By using a scale of 2cm to 1 unit on the xaxis and 2cm to 5 units on the yaxis, draw the graph of y =
2x^{2} – x – 3 for –2 ≤ x ≤ 5.
(c) From your graph, find
(i) The value of y
when x = 3.9,
(ii) The value of x
when y = 31.
(d) Draw a suitable straight line on your graph to find
the values of x which satisfy the equation 2x^{2}
– 3x = 10 for –2 ≤ x ≤ 5.
Solution:
(a)
y
= 2x^{2} – x – 3
when x =
–1,
m
= 2 (–1)^{2} – (–1) – 3 = 0
when x =
4,
n
= 2 (4)^{2} – (4) – 3 = 25
(b)
(c)
(i) From the graph, when x = 3.9, y = 23.5
(ii) From the graph, when y = 31, x = 4.4
(d)
y
= 2x^{2} – x – 3  (1)
2x^{2}
– 3x = 10  (2)
y
= 2x^{2} – x – 3  (1)
0 = 2x^{2}
– 3x – 10  (2) ← (Rearrange (2))
(1) –
(2) : y = 2x + 7
The suitable straight line is y = 2x + 7.
Determine the xcoordinates
of the two points of intersection of the curve
y = 2x^{2} – x – 3 and the straight line y = 2x
+ 7.
x

0

4

y
= 2x + 7

7

15

From the graph, x
= –1.6, 3.1