Deck 3: Polynomial and Rational Functions

Question 1

Write the standard form of the equation of the parabola that has a vertex at and passes through the point .

A)
B)
C)
D)
E)

Answer 1

Question 2

Graph the given function.

A)
B)
C)
D)
E)

Answer 2

Question 3

Write in the form when .

A)
B)
C)
D)
E)

Answer 3

Question 4

Using a graphing utility, graph and approximate the zeros and their multiplicity.

A)
B)
C)
D)
E)

Question 5

Write the standard form of the equation of the parabola that has a vertex at and passes through the point .

A)
B)
C)
D)
E)

Question 6

Use Descartes' Rule of Signs to determine the possible number of positive and negative zeros of .

A)3 positive reals or 1 positive real; no negative reals
B)no positive reals; no negative reals
C)1 positive real; 3 negative reals or 1 negative real
D)3 positive reals or 1 positive real; 3 negative reals or 1 negative real
E)0 positive real; 3 negative reals or 1 negative real

Question 7

If is a root of , use synthetic division to factor the polynomial completely and list all real solutions of the equation.

A) ;
B) ;
C) ;
D) ;
E) ;

Question 8

A farmer has 240 feet of fencing and wants to build two identical pens for his prize-winning pigs. The pens will be arranged as shown. Determine the dimensions of a pen that will maximize its area.

A)
B)
C)
D)
E)

Question 9

Use synthetic division to divide.

A)
B)
C)
D)
E)

Question 10

Use Descartes' Rule of Signs to determine the possible number of positive and negative zeros of .

A)3 positive reals or 1 positive real; 3 negative reals or 1 negative real
B)3 positive reals or 1 positive real; no negative reals
C)no positive reals; no negative reals
D)3 positive reals or 1 positive real; 1 negative real
E)1 positive real; 3 negative reals or 1 negative real

Question 11

An open box is to be made from a square piece of cardboard, 35 inches on a side, by cutting equal squares with sides of length x from the corners and turning up the sides (see figure below). Determine the function, V, in terms of x, that represents the volume of the box.

A)
B)
C)
D)
E)

Question 12

Use long division to divide.

A)
B)4x - 1
C)
D)
E)

Question 13

Find the standard form of the quadratic function shown below:

A)
B)
C)
D)
E)

Question 14

Find all the real zeros of .

A)
B)
C)
D)
E)

Question 15

Determine the vertex of the graph of the quadratic function .

A)
B)
C)
D)
E)

Question 16

Find all real zeros of the polynomial and determine the multiplicity of each.

A)
B)
C)
D)
E)

Question 17

Using the factors and , find the remaining factor(s) of and write the polynomial in fully factored form.

A)
B)
C)
D)
E)

Question 18

Find all the real zeros of .

A)
B)
C)
D)
E)

Question 19

Find all real zeros of the polynomial and determine the multiplicity of each.

A)
B)
C)
D)
E)

Question 20

Find all the rational zeros of the function .

A)
B)
C)
D)
E)

Question 21

Determine the zeros (if any) of the rational function .

A)
B)
C)no zeros
D)
E)

Question 22

Determine the vertex of the graph of the quadratic function .

A)
B)
C)
D)
E)

Question 23

Write the standard form of the equation of the parabola that has a vertex at and passes through the point .

A)
B)
C)
D)
E)

Question 24

Write as a product of linear factors.

A)
B)
C)
D)
E)

Question 25

Use synthetic division to divide.

A)
B)
C)
D)
E)

Question 26

Use long division to divide.

A)
B)
C)
D)
E)4x - 3

Question 27

Find all real zeros of the polynomial and determine the multiplicity of each.

A)
B)
C)
D)
E)

Question 28

An open box is to be made from a square piece of cardboard, 35 inches on a side, by cutting equal squares with sides of length x from the corners and turning up the sides (see figure below). Determine the function, V, in terms of x, that represents the volume of the box.

A)
B)
C)
D)
E)

Question 29

If is a root of , use synthetic division to factor the polynomial completely and list all real solutions of the equation.

A) ;
B) ;
C) ;
D) ;
E) ;

Question 30

Write the standard form of the equation of the parabola that has a vertex at and passes through the point .

A)
B)
C)
D)
E)

Question 31

Write as a product of linear factors.

A)
B)
C)
D)
E)

Question 32

Find all real zeros of the polynomial and determine the multiplicity of each.

A)
B)
C)
D)
E)

Question 33

Find all zeros of the function .

A)
B)
C)
D)
E)

Question 34

Using a graphing utility, graph and approximate the zeros and their multiplicity.

A)
B)
C)
D)
E)

Question 35

Using the factors and , find the remaining factor(s) of and write the polynomial in fully factored form.

A)
B)
C)
D)
E)

Question 36

A farmer has 240 feet of fencing and wants to build two identical pens for his prize-winning pigs. The pens will be arranged as shown. Determine the dimensions of a pen that will maximize its area.

A)
B)
C)
D)
E)

Question 37

Write in the form when .

A)
B)
C)
D)
E)

Question 38

Graph the given function.

A)
B)
C)
D)
E)

Question 39

Find all zeros of the function .

A)
B)
C)
D)
E)

Question 40

Find the standard form of the quadratic function shown below:

A)
B)
C)
D)
E)

Question 41

Write as a product of linear factors.

A)
B)
C)
D)
E)

Question 42

Determine the zeros (if any) of the rational function .

A)no zeros
B)
C)
D)
E)

Question 43

Find all the real zeros of .

A)
B)
C)
D)
E)

Question 44

Write as a product of linear factors.

A)
B)
C)
D)
E)

Question 45

Find all the real zeros of .

A)
B)
C)
D)
E)

Question 46

Use Descartes' Rule of Signs to determine the possible number of positive and negative zeros of .

A)3 positive reals or 1 positive real; no negative reals
B)1 positive real; 3 negative reals or 1 negative real
C)3 positive reals or 1 positive real; 3 negative reals or 1 negative real
D)no positive reals; no negative reals
E)0 positive real; 3 negative reals or 1 negative real

Question 47

Graph the given function.

A)
B)
C)
D)
E)

Question 48

Determine the vertex of the graph of the quadratic function .

A)
B)
C)
D)
E)

Question 49

Find all the rational zeros of the function .

A)
B)
C)
D)
E)

Question 50

A farmer has 336 feet of fencing and wants to build two identical pens for his prize-winning pigs. The pens will be arranged as shown. Determine the dimensions of a pen that will maximize its area.

A)
B)
C)
D)
E)

Question 51

Find all real zeros of the polynomial and determine the multiplicity of each.

A)
B)
C)
D)
E)

Question 52

Find all real zeros of the polynomial and determine the multiplicity of each.

A)
B)
C)
D)
E)

Question 53

Find all zeros of the function .

A)
B)
C)
D)
E)

Question 54

Write the standard form of the equation of the parabola that has a vertex at and passes through the point .

A)
B)
C)
D)
E)

Question 55

An open box is to be made from a square piece of cardboard, 21 inches on a side, by cutting equal squares with sides of length x from the corners and turning up the sides (see figure below). Determine the function, V, in terms of x, that represents the volume of the box.

A)
B)
C)
D)
E)

Question 56

Using a graphing utility, graph and approximate the zeros and their multiplicity.

A)
B)
C)
D)
E)

Question 57

Write the standard form of the equation of the parabola that has a vertex at and passes through the point .

A)
B)
C)
D)
E)

Question 58

Find the standard form of the quadratic function shown below:

A)
B)
C)
D)
E)

Question 59

Find all zeros of the function .

A)
B)
C)
D)
E)

Question 60

Use Descartes' Rule of Signs to determine the possible number of positive and negative zeros of .

A)3 positive reals or 1 positive real; 1 negative real
B)3 positive reals or 1 positive real; no negative reals
C)no positive reals; no negative reals
D)1 positive real; 3 negative reals or 1 negative real
E)3 positive reals or 1 positive real; 3 negative reals or 1 negative real

Question 61

Find all the rational zeros of the function .

A)
B)
C)
D)
E)

Question 62

Find all zeros of the function .

A)
B)
C)
D)
E)

Question 63

Use synthetic division to divide.

A)
B)
C)
D)
E)

Question 64

Find all the real zeros of .

A)
B)
C)
D)
E)

Question 65

Write as a product of linear factors.

A)
B)
C)
D)
E)

Question 66

Write in the form when .

A)
B)
C)
D)
E)

Question 67

Find all zeros of the function .

A)
B)
C)
D)
E)

Question 68

Using the factors and , find the remaining factor(s) of and write the polynomial in fully factored form.

A)
B)
C)
D)
E)

Question 69

Find the vertex of the parabola. y = 9x² - 10

A)(0, -10)
B)(0, 9)
C)(9, -10)
D)(-10, 0)
E)(-10, 9)

Question 70

Use Descartes' Rule of Signs to determine the possible number of positive and negative zeros of .

A)3 positive reals or 1 positive real; 3 negative reals or 1 negative real
B)3 positive reals or 1 positive real; no negative reals
C)1 positive real; 3 negative reals or 1 negative real
D)3 positive reals or 1 positive real; 1 negative real
E)no positive reals; no negative reals

Question 71

Graph the quadratic function.

A)
B)
C)
D)

Question 72

If is a root of , use synthetic division to factor the polynomial completely and list all real solutions of the equation.

A) ;
B) ;
C) ;
D) ;
E) ;

Question 73

Find all the real zeros of .

A)
B)
C)
D)
E)

Question 74

Write as a product of linear factors.

A)
B)
C)
D)
E)

Question 75

Determine the zeros (if any) of the rational function .

A)
B)
C)
D)
E)no zeros

Question 76

Use long division to divide.

A)
B)
C)
D)
E)-x + 2

Question 77

Find the vertex of the parabolic graph of the equation. y = 6(x - 7) ² + 4

A)(49, 4)
B)(7, 6)
C)(4, 7)
D)(7, 4)
E)(7, 0)

Question 78

Graph the quadratic function. f (x) = x² + 3x

A)
B)
C)
D)

Question 79

Graph the quadratic function. f (x) = - 3x² + 2

A)
B)
C)
D)

Question 80

Use Descartes' Rule of Signs to determine the possible number of positive and negative zeros of .

A)3 positive reals or 1 positive real; 3 negative reals or 1 negative real
B)3 positive reals or 1 positive real; no negative reals
C)0 positive real; 3 negative reals or 1 negative real
D)1 positive real; 3 negative reals or 1 negative real
E)no positive reals; no negative reals