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Sketching Polynomials
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January 16, 2009
Oct 11 9:12 AM
Sketching Polynomial Functions
Objective Sketch the graphs of Polynomial
Functions
Sketching Polynomials
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January 16, 2009
Oct 11 9:12 AM
Identify the shape and degree of each graph:
shape shape shape shape
f(x) = 3x+2 f(x) = (x2) f(x) = x + 1 f(x) = x(x2) (x+2)2 3 2
degree degree degree degree
Sketching Polynomials
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January 16, 2009
Oct 11 9:12 AM
Steps to Graphing Polynomials:
Example: f(x) = (x + 3)(x 4x 5)2
Sketching Polynomials
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Oct 11 9:12 AM
Step 1: Find the degree &
determine the shape.
f(x) = (x + 3)(x 4x 5)2
Sketching Polynomials
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January 16, 2009
Oct 11 9:12 AM
Step 2: Write the function in factored form.
f(x) = (x + 3)(x 5)(x + 1)
f(x) = (x + 3)(x 4x 5)2
Sketching Polynomials
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January 16, 2009
Oct 11 9:12 AM
Step 3: Identify the zeros (roots).
(x + 3) = 0 (x 5) = 0 (x + 1) = 0
Sketching Polynomials
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January 16, 2009
Oct 11 9:12 AM
Step 4: Graph the zeros.
5 10510
Sketching Polynomials
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January 16, 2009
Oct 11 9:12 AM
Step 5: Find the midpoint of each pair of zeros.
x y
3 0
1 0
5 0
f(x) = (x + 3)(x 5)(x + 1)
Sketching Polynomials
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January 16, 2009
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Step 6: Find f(midpoint).
x y
3 0
1 0
5 0
2
2
y = (x + 3)(x 4x 5)2
Sketching Polynomials
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January 16, 2009
Oct 11 9:12 AM
Step 7: Graph (midpoint, f(midpoint)).
5 10510
45
7
Sketching Polynomials
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Oct 11 9:12 AM
Step 8: Determine the end behavior of the graph.
5 10510
45
7y = (x + 3)(x 4x 5)
Leading Coefficient:
Degree:
End Behavior:
Sketching Polynomials
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January 16, 2009
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Step 9: Connect the points to make a curve.
10 5 5 10
7
45
Sketching Polynomials
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January 16, 2009
Oct 11 9:12 AM
Relative Maximum & Relative Minimum.
10 5 5 10
7
45
relative max
relative min
Sketching Polynomials
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January 16, 2009
Oct 11 9:12 AM
Follow the steps to graph the
Polynomial:
Example: f(x) = x(x + 4) (x 2)2
Sketching Polynomials
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January 16, 2009
Oct 11 9:12 AM
Example: f(x) = x(x + 4) (x 2)2
Sketching Polynomials
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January 16, 2009
Oct 11 9:12 AM
Example: f(x) = x(x + 4) (x 2)2
25
32
Sketching Polynomials
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January 16, 2009
Oct 11 9:12 AM
Example: f(x) = x(x + 4) (x 2)2
25
32
Sketching Polynomials
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January 16, 2009
Oct 11 9:12 AM
Follow the steps to graph the
Polynomial:
Example: f(x) = x(x + 2)2(x 2)
Sketching Polynomials
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January 16, 2009
Oct 11 9:12 AM
Example: f(x) = x(x + 2)2(x 2)
Sketching Polynomials
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January 16, 2009
Oct 11 9:12 AM
Example: f(x) = x(x + 2)2(x 2)
Sketching Polynomials
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January 16, 2009
Oct 11 9:12 AM
Homework:1/2 sheet
Sketching PolynomialFunctions