Sketching Polynomials
January 16, 2009
Sketching Polynomial Functions Objective Sketch the graphs of Polynomial Functions
Oct 11 9:12 AM
1
Sketching Polynomials
January 16, 2009
Identify the shape and degree of each graph: f(x) = 3x+2
f(x) = (x2)2 f(x) = x3+ 1
2
f(x) = x(x2) (x+2)
shape
shape
shape
shape
degree
degree
degree
degree
Oct 11 9:12 AM
2
Sketching Polynomials
January 16, 2009
Steps to Graphing Polynomials: Example: f(x) = (x + 3)(x 2 4x 5)
Oct 11 9:12 AM
3
Sketching Polynomials
January 16, 2009
Step 1: Find the degree & determine the shape.
f(x) = (x + 3)(x2 4x 5)
Oct 11 9:12 AM
4
Sketching Polynomials
January 16, 2009
Step 2: Write the function in factored form.
f(x) = (x + 3)(x 2 4x 5) f(x) = (x + 3)(x 5)(x + 1)
Oct 11 9:12 AM
5
Sketching Polynomials
January 16, 2009
Step 3: Identify the zeros (roots).
(x + 3) = 0
(x 5) = 0
(x + 1) = 0
Oct 11 9:12 AM
6
Sketching Polynomials
January 16, 2009
Step 4: Graph the zeros. 10
5
5
10
Oct 11 9:12 AM
7
Sketching Polynomials
January 16, 2009
Step 5: Find the midpoint of each pair of zeros. x
y f(x) = (x + 3)(x 5)(x + 1)
3
0
1
0
5
0
Oct 11 9:12 AM
8
Sketching Polynomials
January 16, 2009
Step 6: Find f(midpoint). y = (x + 3)(x2 4x 5)
x 3 2 1 2 5
y 0 0
0
Oct 11 9:12 AM
9
Sketching Polynomials
January 16, 2009
Step 7: Graph (midpoint, f(midpoint)). 7 10
5
5
10
45
Oct 11 9:12 AM
10
Sketching Polynomials
January 16, 2009
Step 8: Determine the end behavior of the graph. y = (x + 3)(x 4x 5) 7 10
5
5
45
10
Leading Coefficient: Degree: End Behavior:
Oct 11 9:12 AM
11
Sketching Polynomials
January 16, 2009
Step 9: Connect the points to make a curve. 7 10
5
5
10
45
Oct 11 9:12 AM
12
Sketching Polynomials
January 16, 2009
Relative Maximum & Relative Minimum. relative max
7 10
5
5
45
10
relative min
Oct 11 9:12 AM
13
Sketching Polynomials
January 16, 2009
Follow the steps to graph the Polynomial: 2
Example: f(x) = x(x + 4) (x 2)
Oct 11 9:12 AM
14
Sketching Polynomials
January 16, 2009
Example: f(x) = x(x + 4)2(x 2)
Oct 11 9:12 AM
15
Sketching Polynomials
January 16, 2009
Example: f(x) = x(x + 4)2(x 2) 32
25
Oct 11 9:12 AM
16
Sketching Polynomials
January 16, 2009
2
Example: f(x) = x(x + 4) (x 2) 32
25
Oct 11 9:12 AM
17
Sketching Polynomials
January 16, 2009
Follow the steps to graph the Polynomial: Example: f(x) = x(x + 2)2(x 2)
Oct 11 9:12 AM
18
Sketching Polynomials
January 16, 2009
Example: f(x) = x(x + 2)2(x 2)
Oct 11 9:12 AM
19
Sketching Polynomials
January 16, 2009
Example: f(x) = x(x + 2)2(x 2)
Oct 11 9:12 AM
20
Sketching Polynomials
January 16, 2009
Homework: 1/2 sheet Sketching Polynomial Functions
Oct 11 9:12 AM
21