Transition Year Maths Example 3 x x3


–3x2 –4x +12 y


Draw a graph of the curve y = x3 from x = –3 to x = +3


–3


–27 –27 12 12


–30


–2 –8


–12 8


12 0


–1 –1 –3 4


12 12 y


0 0 0 0


12 12


–3x2 –4x + 12


1 1


–3 –4 12 6


2 8


–12 –8 12 0


3 27


–27 –12 12 0


x


Closed Shapes


When both the x and the y are squared, new shapes are formed. Square roots are estimated to one place of decimals.


1. Circles: x2 + y2 = 9. Find points on the graph.


Let x = 0 ⇒ y2 Let y = 0 ⇒ x2


Let x = 1 ⇒ 1 + y2 Let y = 1 ⇒ x2


Let x = –1 ⇒ 1 + y2 Let y = –1 ⇒ x2


= 9 ⇒ y = +3 or y = –3 ⇒ (0,3) and (0,–3) are on the graph. = 9 ⇒ x = +3 or x = –3 ⇒ (3, 0) and (–3, 0) are on the graph. = 9 ⇒ y2


+ 1 = 9 ⇒ x2 = 9 ⇒ y2


+1 = 9 ⇒ x2


± 8 ± 8


= 8 ⇒, 2·8) and (–1,–2·8) are on the graph. = 8 ⇒ (2·8,–1) and (–2·8,–1) are on the graph.


= 8 ⇒ y = ⇒(1, 2·8) and (1, –2·8) are on the graph. = 8 ⇒ x = ⇒ (2·8,1) and (–2·8,1)


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