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```					    Graphing Cubic Polynomials
   Identify various types of cubic curves
(Refer to Excel Applet for Cubic Curves)

   Sketch simple cubic curves

   Form equation of cubic polynomial from
sketch
Graphing Cubic Polynomials
The real roots of the polynomial equation P(x) = 0 are
given by the values of the intercepts of the function
y = P(x) with the x-axis.

Nature of roots:
3 real and distinct  x = x1, x = x2 and x= x3 are the
solutions.
2 real and equal and 1 real and distinct
1 real and 2 complex roots
Definition of Cubic Function
A cubic function is a polynomial function of the form
ax3 + bx2 + cx + d, where a, b, c and d are constants
and a cannot be 0.

10

Example 1: y = x3
5

0
-4    -2         0   2   4

-5

-10
Use the excel applet to investigate

Example 2: y = x3 – 5x2 + 2x + 8

10

5

0

-4    -2             0   2   4

-5

-10
Use the excel applet to investigate

Example 3: y = x3 – x2 - x +1

10

5

0
-2    -1         0   1   2     3   4

-5

-10
Graphing Cubic Polynomials
How to graph a cubic function?
Example : y = x3 – 2x2 –x + 2 (Note: a > 0)
Step 1: Check if y can be factorise into 3 linear factors
y = (x + 1)(x -2)(x -1)
(Sometimes, you may get 1 linear factor and a
quadratic factor that cannot be factorised
When this happens – use the quadratic formula to solve
for x. If it cannot be solved, then there will be 2
complex roots and 1 real root)
Step 2: Set y = 0, x = -1, x = 2, x = 1
Graphing Cubic Polynomials
Step 3: Finding the y-intercept.
When x = 0, y = 2.  (0, 2)
y = x3 – 2x2 –x + 2

```
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