Sketching Polynomials - Mrs. Motichka

Sketching Polynomials

January 16, 2009

Sketching Polynomial Functions Objective ­ Sketch the graphs of Polynomial Functions

Oct 11 ­ 9:12 AM

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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

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Sketching Polynomials

January 16, 2009

Steps to Graphing Polynomials: Example: f(x) = (x + 3)(x 2 ­ 4x ­ 5)

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Sketching Polynomials

January 16, 2009

Step 1: Find the degree & determine the shape.

f(x) = (x + 3)(x2 ­ 4x ­ 5)

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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)

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Sketching Polynomials

January 16, 2009

Step 3: Identify the zeros (roots).

(x + 3) = 0

(x ­ 5) = 0

(x + 1) = 0

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Sketching Polynomials

January 16, 2009

Step 4: Graph the zeros. ­10

­5

5

10

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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

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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

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Sketching Polynomials

January 16, 2009

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

7 ­10

­5

5

10

­45

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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:

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11

Sketching Polynomials

January 16, 2009

Step 9: Connect the points to make a curve.

7 ­10

5

­5

10

­45

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Sketching Polynomials

January 16, 2009

Relative Maximum & Relative Minimum. relative max

7 ­10

5

­5

­45

10

relative min

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Sketching Polynomials

January 16, 2009

Follow the steps to graph the Polynomial: 2

Example: f(x) = x(x + 4) (x ­ 2)

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Sketching Polynomials

January 16, 2009

Example: f(x) = x(x + 4)2(x ­ 2)

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Sketching Polynomials

January 16, 2009

Example: f(x) = x(x + 4)2(x ­ 2) 32

­25

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Sketching Polynomials

January 16, 2009

2

Example: f(x) = x(x + 4) (x ­ 2) 32

­25

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Sketching Polynomials

January 16, 2009

Follow the steps to graph the Polynomial: Example: f(x) = ­x(x + 2)2(x ­ 2)

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Sketching Polynomials

January 16, 2009

Example: f(x) = ­x(x + 2)2(x ­ 2)

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Sketching Polynomials

January 16, 2009

Example: f(x) = ­x(x + 2)2(x ­ 2)

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Sketching Polynomials

January 16, 2009

Homework: 1/2 sheet Sketching Polynomial Functions

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