Polynomials

1
Polynomials

• Working with indices
• The cubic function

2
Indices - revision

• Page 78
• Exercise A
• Q1-4

3
The Cubic Function y x3
y x3
This is the basic shape of a cubic
4
The Cubic Function y ax3
y 2x3
The coefficient of x3 gives the steepness of
the curve
y 0.5x3
y x3
5
The Cubic Function y (x-k)3
The function y(x-k)3 is a translation of k
along the x-axis
y x3
y (x3)3
When y0 (x3)0 x-3
y (x-2)3
6
The Cubic Function y x3 d
The function yx3 d is a translation of d
along the y-axis
y x3
y x3 3
y x3 - 6
When x0 y3
When x0 y-6
7
The Cubic Function y (x-k)3 d
The function y(x-k)3 d is a translation of k
along the x-axis and d along the y-axis
y x3
y (x-2)3 3
k d
in vector notation
y (x3)3 - 2
8
Whats my equation ?
y x3
k
d
y(x- k)3 d
y (x - -2)3 4
y (x 2)3 4
9
Whats my equation (2) ?
y x3
k
d
y(x- k)3 d
y (x - 3)3 - 2
10
Have a go

• Page 79 Cubic Graphs
• Section B questions
• B6, B7, B8, B9

11
Plenary - Sketch the Cubic Function y x3
2x2 2x 6
OK, thats a bit tough . It is the same as y
(x-3)(x-1)(x2)
If (x-3)0, x3, y0 If (x-1)0, x1, y0 If
(x2)0, x-2, y0
It goes through all these points