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# Quadratic Functions - PowerPoint PPT Presentation

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

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Presentation Transcript

Functions

Polynomial

Functions &

Graphs

Synthetic

Divison

Zeros of

Polynomial

Functions

More on

Zeros of

Polynomials

Solving

Inequalities

Functions

Polynomial

Functions &

Graphs

Synthetic

Division

Zeros of

Polynomial

Functions

More on

Polynomial

Zeros

Solving

Inequalities

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The function for this graph is

f(x) = (x – 5)2 – 1.

What is

f(x) = -(x – 3)2 – 4?

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.

Yes.

Degree = 7

Does the graph

represent a

polynomial function?

f(x) = 6x3 + 3x2 – 3x - 1

Up to the right,

Down to the left.

-1, multiplicity 1

1, multiplicity 2

Find f(-3) given

f(x) = 4x3 – 6x2 – 5x + 6

Solve the equation

3x3 – 28x2 + 51x – 14 = 0

given that 2 is one solution.

Use synthetic division to find all zeros of

f(x) = x3 – 3x2 – 18x + 40.

f(x) = 3x3 – 17x2 + 18x + 8

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

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

1 positive real zero

1 negative real zero

Give all the roots of

f(x) = x3 + 5x2 + 12x – 18

Use the graphing calculator to determine the zeros of

f(x) = x3 – 6x2 – x + 6

1, 3, 4, or 5

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

Find all roots of the equation.

Hint: -2i is one root.

x4 – 21x2 – 100 = 0

f(x) = x4 – 3x2 – 4

Factor completely.

f(x) = x3 + 4x2 – x - 4

Daily

Double!!

f(x)= (x – 2)(x + 2)(x –3)

(x – 3)(x + 2) > 0

x2 + 3x – 18 > 0

x2 – 2x – 24 < 0

x2 – 3x – 10 < 0

x2 + 6x< – 8

Double

Jeopardy!!

Final

Jeopardy

Graphs of Polynomials

Give the equation for the function.

-10 < x < 10

-10 < y < 60