Powerpoint Jeopardy Quadratic & Polynomial Functions & Models Rational Functions &...

Powerpoint JeopardyQuadratic & Polynomial Functions &

Models

Rational Functions &

Models

Polynomial & Rational

Inequalities

Real Zeros of a Polynomial

Function

Complex Zeros

10 10 10 10 10

20 20 20 20 20

30 30 30 30 30

40 40 40 40 40

50 50 50 50 50

Is this function a polynomial function?If it is, give its degree. If it is not, tell whynot.

5

3

2( )

xf x

x

Find the coordinates of the vertex of theparabola.

2( ) 8 25f x x x

For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at each x-intercept.

22 51

( ) ( 5)2

f x x x

Construct a polynomial where the graph crosses the x-axis at -2 and 3, touches the x-axis at 5, crosses the y-axis at -5 and is below the x-axis between -2 and 3.

The manufacturer of a CD player has found the revenue R ( in dollars) is

when the unit price p dollars. If the manufacturer sets the price p to maximize revenue, what is the maximum revenue to the nearest dollar?

24 1810R p p

Find the domain of

2

2

20( )

14 48

x xR x

x x

What is the equation of the vertical asymptote(s) of the function

2

5( )

9

xf x

x

What is the equation of the oblique asymptote of the function

2 7 9( )

7

x xf x

x

Find the vertical asymptote(s) and/or hole(s) for

2

2

6( )

12

x xR x

x x

Graph the function

2( )

49

xf x

x

Solve the inequality

3 23 28 0x x x

Solve the inequality. Write your answer in interval notation.

1 22

1

x

x x

The revenue achieved by selling x graphing calculators is figured to be x (29 – 0.2x) dollars. The cost of each calculator is $17. How many graphing calculators must be sold to make a profit (revenue – cost) of at least $167.20?

Solve the given rational inequality

2 51

3

x

x

A rare species of insect was discovered in the rain forest of Costa Rica. Environmentalists transplant the insect into a protected area. The population of the insect t months after being transplanted is

(a) What was the population when t = 0?(b) What will the population be after 10 years.(c) What is the largest value the population could reach?

45(1 0.6 )( )

(3 0.02 )

tP t

t

Find the real solutions of the equation

3 23 3 1 0x x x

Find the real solutions of the equation.

3 27 15 9 0x x x

Use the intermediate value theorem to show that the polynomial has a real zero in the interval [-1, 0].

3 2( ) 7 5 10 9f x x x x

Find the rational zeros of

List any irrational zeros correct to two decimal places.

3 2( ) 2 5 6f x x x x

Find the rational zeros of the polynomial

List any irrational zeros correct to two decimal places

3 2( ) 2 9 18f x x x x

Given the complex polynomial f(x) whose coefficients are real numbers, find the remaining zeros of f.

Degree 3; zeros: 5, 2 – i

Find a third degree polynomial function with real coefficients and with zeros 1 and 3 + i.

Find a third degree polynomial function with real coefficients and with zeros – 2 and 3 + i.

For the polynomialone zero is -2i. Find all others.

4 2( ) 21 100P x x x

Find the complex zeros of the polynomial function

4 3 2( ) 8 16 8 17f x x x x x