year 8 maths

7I
Non-linear graphs
451
6 What are the lowest and highest values of y on a graph of these rules if x ranges from −3 to 3 ?
a y = x 2
b y = x 2 − 10
c y = 6 − x 2
d y = x 3
e y = −x 3 − 1
f y = (x − 1) 3
7 Here are some rules classified by the name of their graph.
Line Parabola Hyperbola Exponential
y = 2x − 3 y = x 2 y = 1 x
y = −5x + 1 y = 3 − x 2 y = − 5 x
y = 3 x
y = 4 x − 3
Name the type of graph that is produced by each of these rules.
a y = x 2 + 7
b y = −2x + 4
c
d
y = 2 x
y = 7 x
e y = − 3 x + 1
f y = 4 − x 2
g y = 1 − x
h y = (0.5) x
ENRICHMENT
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8
Families of parabolas
8 For each family of parabolas, plot graphs by hand or use technology to draw each set on the same
set of axes. Then describe the features of each family. Describe the effect on the graph when the
number a changes.
a Family 1: y = ax 2 Use a = 1 , a = 1, a = 2 and a = 3 .
2
b Family 2: y = −ax 2 Use a = 1 , a = 1, a = 2 and a = 3 .
2
c Family 3: y = x 2 + a Use a = −3, a = −1, a = 0, a = 2 and a = 5 .
d Family 4: y = (x − a) 2 Use a = −2, a = 0, a = 1 and a = 4 .
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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