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Quadratic Functions. Polynomial Functions & Graphs. Synthetic Divison. Zeros of Polynomial Functions. More on Zeros of Polynomials. Solving Inequalities. Quadratic Functions. Polynomial Functions & Graphs. Synthetic Division. Zeros of Polynomial Functions. More on

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Presentation Transcript
slide2

Quadratic

Functions

slide3

Polynomial

Functions &

Graphs

slide4

Synthetic

Divison

slide5

Zeros of

Polynomial

Functions

slide6

More on

Zeros of

Polynomials

slide7

Solving

Inequalities

slide8

Quadratic

Functions

Polynomial

Functions &

Graphs

Synthetic

Division

Zeros of

Polynomial

Functions

More on

Polynomial

Zeros

Solving

Inequalities

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slide13

The function for this graph is

f(x) = (x – 5)2 – 1.

slide16

What is

f(x) = -(x – 3)2 – 4?

slide17

The cost in millions of dollars for a company to manufacture x thousand automobiles is given by the function

C(x) = 3x2 – 18x + 63. Find the number of automobiles that must be produced to minimize the cost.

slide20

Yes.

Degree = 7

slide21

Does the graph

represent a

polynomial function?

slide23

Use the leading coefficient test to determine the end behavior for

f(x) = 6x3 + 3x2 – 3x - 1

slide24

Up to the right,

Down to the left.

slide26

-1, multiplicity 1

1, multiplicity 2

slide33

Find f(-3) given

f(x) = 4x3 – 6x2 – 5x + 6

slide35

Solve the equation

3x3 – 28x2 + 51x – 14 = 0

given that 2 is one solution.

slide37

Use synthetic division to find all zeros of

f(x) = x3 – 3x2 – 18x + 40.

slide41

Use the rational zeros theorem to list all possible rational zeros of

f(x) = 3x3 – 17x2 + 18x + 8

and then use this root to find all zeros of the function.

slide43

Use Descartes’ Rule of Signs to determine the possible number of positive real zeros and negative real zeros for f(x) = x6 – 8.

slide44

1 positive real zero

1 negative real zero

slide45

Give all the roots of

f(x) = x3 + 5x2 + 12x – 18

slide47

Use the graphing calculator to determine the zeros of

f(x) = x3 – 6x2 – x + 6

1, 3, 4, or 5

slide49

Use the Upper Bound Theorem to determine which of the following is a good upper bound for

f(x) = x4 + x3 – 7x2 – 5x + 10

1, 3, 4, or 5

slide51

Find all roots of the equation.

Hint: -2i is one root.

x4 – 21x2 – 100 = 0

slide55

Factor completely.

f(x) = x3 + 4x2 – x - 4

slide57

Daily

Double!!

slide59

f(x)= (x – 2)(x + 2)(x –3)

Other answers are possible.

slide70

Double

Jeopardy!!

slide72

Final

Jeopardy

Graphs of Polynomials

slide73

Give the equation for the function.

-10 < x < 10

-10 < y < 60

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