Sketching Polynomials 

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Sketching Polynomial Functions

Objective ­ Sketch the graphs of Polynomial

Functions

Sketching Polynomials 

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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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Steps to Graphing Polynomials:

Example: f(x) = (x + 3)(x ­ 4x ­ 5)2

Sketching Polynomials 

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Step 1: Find the degree &

determine the shape.

f(x) = (x + 3)(x ­ 4x ­ 5)2

Sketching Polynomials 

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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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Step 3: Identify the zeros (roots).

(x + 3) = 0 (x ­ 5) = 0 (x + 1) = 0

Sketching Polynomials 

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Step 4: Graph the zeros.

5 10­5­10

Sketching Polynomials 

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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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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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Step 7: Graph (midpoint, f(midpoint)).

5 10­5­10

­45

7

Sketching Polynomials 

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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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Step 9: Connect the points to make a curve.

­10 ­5 5 10

7

­45

Sketching Polynomials 

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Relative Maximum & Relative Minimum.

­10 ­5 5 10

7

­45

relative max

relative min

Sketching Polynomials 

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Follow the steps to graph the

Polynomial:

Example: f(x) = x(x + 4) (x ­ 2)2

Sketching Polynomials 

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Example: f(x) = x(x + 4) (x ­ 2)2

Sketching Polynomials 

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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

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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

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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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Homework:1/2 sheet

Sketching PolynomialFunctions