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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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Quadratic functions

Quadratic

Functions


Quadratic functions

Polynomial

Functions &

Graphs


Quadratic functions

Synthetic

Divison


Quadratic functions

Zeros of

Polynomial

Functions


Quadratic functions

More on

Zeros of

Polynomials


Quadratic functions

Solving

Inequalities


Quadratic functions

Quadratic

Functions

Polynomial

Functions &

Graphs

Synthetic

Division

Zeros of

Polynomial

Functions

More on

Polynomial

Zeros

Solving

Inequalities

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Quadratic functions

What is y = (x + 1)2?




Quadratic functions

The function for this graph is

f(x) = (x – 5)2 – 1.




Quadratic functions

What is

f(x) = -(x – 3)2 – 4?


Quadratic functions

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.




Quadratic functions

Yes. give the degree.

Degree = 7


Quadratic functions

Does the graph give the degree.

represent a

polynomial function?


Quadratic functions

Yes give the degree.


Quadratic functions

Use the leading coefficient test to determine the end behavior for

f(x) = 6x3 + 3x2 – 3x - 1


Quadratic functions

Up to the right, behavior for

Down to the left.


Quadratic functions

Find the zeros and their multiplicities of the function. behavior for

F(x) = 4(x + 5)(x – 1)2


Quadratic functions

-1, multiplicity 1 behavior for

1, multiplicity 2


Quadratic functions

Graph the function. behavior for F(x) = x2(x – 3)(x – 2)


Quadratic functions

Use synthetic division to divide. behavior for

3x2 + 29x + 56

x + 7


Quadratic functions

3 behavior for x + 8



Quadratic functions

x behavior for 4 + 2x3 + 5x2 + 10x + 20. R. 45


Quadratic functions

Find behavior for f(-3) given

f(x) = 4x3 – 6x2 – 5x + 6


Quadratic functions

-141 behavior for


Quadratic functions

Solve the equation behavior for

3x3 – 28x2 + 51x – 14 = 0

given that 2 is one solution.


Quadratic functions

2, 7, 1/3 behavior for


Quadratic functions

Use synthetic division to find all zeros of behavior for

f(x) = x3 – 3x2 – 18x + 40.


Quadratic functions

2, 5, -4 behavior for



Quadratic functions

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.


Quadratic functions

-1/3, 2, 4 zeros of


Quadratic functions

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


Quadratic functions

1 positive real zero number of positive real zeros and negative real zeros for

1 negative real zero


Quadratic functions

Give all the roots of number of positive real zeros and negative real zeros for

f(x) = x3 + 5x2 + 12x – 18


Quadratic functions

1, -3 + 3 number of positive real zeros and negative real zeros for i, - 3 – 3i


Quadratic functions

Use the graphing calculator to determine the zeros of number of positive real zeros and negative real zeros for

f(x) = x3 – 6x2 – x + 6

1, 3, 4, or 5


Quadratic functions

1, -1, 6 number of positive real zeros and negative real zeros for


Quadratic functions

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


Quadratic functions

3 following is a good upper bound for


Quadratic functions

Find all roots of the equation. following is a good upper bound for

Hint: -2i is one root.

x4 – 21x2 – 100 = 0


Quadratic functions

-2i, 2i, 5, -5 following is a good upper bound for



Quadratic functions

f factors.(x)= (x – 2)(x + 2)(x – i)(x + i)


Quadratic functions

Factor completely. factors.

f(x) = x3 + 4x2 – x - 4


Quadratic functions

f factors.(x)= (x – 1)(x + 1)(x + 4)


Quadratic functions

Daily factors.

Double!!


Quadratic functions

Give an equation for the polynomial function that has zeros of 2, -2, and 3 and has a degree of 3.


Quadratic functions

f of 2, -2, and 3 and has a degree of 3.(x)= (x – 2)(x + 2)(x –3)

Other answers are possible.



Quadratic functions

(- notation.∞, -2) or (3, ∞)



Quadratic functions

(- notation.∞, -6) or (3, ∞)



Quadratic functions

(- notation.4, 6)



Quadratic functions

[-2, 5] notation.



Quadratic functions

[-4, -2] notation.


Quadratic functions

Double notation.

Jeopardy!!


Quadratic functions

Final notation.

Jeopardy

Graphs of Polynomials


Quadratic functions

Give the equation for the function. notation.

-10 < x < 10

-10 < y < 60


Quadratic functions

y notation. = (x – 2)2(x + 3)2