year 8 maths

440 Chapter 7 Linear relationships 1
ENRICHMENT
– –
16
More than one solution
16 a Use this graph of y = x 2 to solve the following
equations.
i x 2 = 4
ii x 2 = 9
iii x 2 = 16
iv x 2 = 25
25
20
y
b Explain why there are two solutions to each of
the equations in part a above.
c
Use digital technology to graph y = x 2 and
graphically solve the following equations,
rounding answers to two decimal places.
i x 2 = 5
ii x 2 = 6.8
iii x 2 = 0.49
iv x 2 = 12.75
v x 2 = 18.795
d Give one reason why the graph of y = x 2 does not give a solution to the equation x 2 = −9 .
e
f
List three more equations of the form x 2 = ‘ a number’ that can’t be solved from the graph of
y = x 2 .
List the categories of numbers that will give a solution to the equation: x 2 = ‘ a number’.
g Graph y = x + 2 and y = x 2 on the same screen and graphically solve x 2 = x + 2 by finding the
x values of the points of intersection.
h Use digital technology to solve the following equations using graphical techniques. Round
answers to two decimal places.
i x 2 = 3x + 16
ii x 2 = 27 − 5x
iii x 2 = 2x − 10
iv x 2 = 6x − 9
15
10
−5 −4 −3 −2 −1
5
O
1
2 3 4 5
x
Cambridge Maths NSW
Stage 4 Year 8 Second edition
ISBN 978-1-108-46627-1 © Palmer et al. 2018
Cambridge University Press
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