powerpoint jeopardy quadratic & polynomial functions & models rational functions &...
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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
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Is this function a polynomial function?If it is, give its degree. If it is not, tell whynot.
5
3
2( )
xf x
x
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Find the coordinates of the vertex of theparabola.
2( ) 8 25f x x x
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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
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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.
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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
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Find the domain of
2
2
20( )
14 48
x xR x
x x
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What is the equation of the vertical asymptote(s) of the function
2
5( )
9
xf x
x
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What is the equation of the oblique asymptote of the function
2 7 9( )
7
x xf x
x
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Find the vertical asymptote(s) and/or hole(s) for
2
2
6( )
12
x xR x
x x
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Graph the function
2( )
49
xf x
x
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Solve the inequality
3 23 28 0x x x
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Solve the inequality. Write your answer in interval notation.
1 22
1
x
x x
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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?
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Solve the given rational inequality
2 51
3
x
x
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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
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Find the real solutions of the equation
3 23 3 1 0x x x
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Find the real solutions of the equation.
3 27 15 9 0x x x
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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
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Find the rational zeros of
List any irrational zeros correct to two decimal places.
3 2( ) 2 5 6f x x x x
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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
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Given the complex polynomial f(x) whose coefficients are real numbers, find the remaining zeros of f.
Degree 3; zeros: 5, 2 – i
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Find a third degree polynomial function with real coefficients and with zeros 1 and 3 + i.
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Find a third degree polynomial function with real coefficients and with zeros – 2 and 3 + i.
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For the polynomialone zero is -2i. Find all others.
4 2( ) 21 100P x x x
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Find the complex zeros of the polynomial function
4 3 2( ) 8 16 8 17f x x x x x