A ball is tossed upward. Its height after t seconds is given in the table. \[\begin{array} { l | r r r r r } \text { Time (seconds) } & 0.5 & 1 & 1.5 & 2 & 2.5 \\ \hline \text { Height (feet) } & 26.5 & 39.5 & 44.5 & 41.5 & 30.5 \end{array}\] Find a quadratic function to model the data. Use the model to determine when the ball reaches its maximum height, as well as the value of the maximum height.

A) The ball reaches a maximum height of 44.6 feet in 1.6 seconds. B) The ball reaches a maximum height of 40 feet in 1.5 seconds. C) The ball reaches a maximum height of 50 feet in 2.1 seconds. D) The ball never reaches a maximum height. A) The ball reaches a maximum height of 44.6 feet in 1.6 seconds. B) The ball reaches a maximum height of 40 feet in 1.5 seconds. C) The ball reaches a maximum height of 50 feet in 2.1 seconds. D) The ball never reaches a maximum height.

Exam 4: Polynomials and Rational Functions

A ball is tossed upward. Its height after t seconds is given in the table. Time (seconds) 0.5 1 1.5 2 2.5 Height (feet) 26.5 39.5 44.5 41.5 30.5 Find a quadratic function to model the data. Use the model to determine when the ball reaches its maximum height, as well as the value of the maximum height.

(Multiple Choice)

4.9/5

(42)

Question 81

Bob owns a watch repair shop. He has found that the cost of operating his shop is given by $c ( x ) = 2 x ^ { 2 } - 156 x + 88$ , where c is cost and x is the number of watches repaired. How many watches must he repair to have the lowest cost?

(Multiple Choice)

4.8/5

(35)

Question 82

What is the domain of the graph?

(Multiple Choice)

4.9/5

(36)

Question 83

Give the equation of any oblique asymptotes. - $f ( x ) = \frac { x ^ { 2 } + 3 x + 5 } { x + 6 }$

(Multiple Choice)

4.7/5

(36)

Question 84

Graph the polynomial function. Factor first if the expression is not in factored form. - $f(x)=x^{3}+4 x^{2}-x-4$ $Graph the polynomial function. Factor first if the expression is not in factored form. - f(x)=x^{3}+4 x^{2}-x-4$

(Multiple Choice)

5.0/5

(27)

Question 85

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary. - $f ( x ) = x ^ { 3 } - 64$

(Multiple Choice)

4.9/5

(32)

Question 86

Use synthetic division to perform the division. $\frac { x ^ { 4 } + 625 } { x - 5 }$

(Multiple Choice)

4.8/5

(40)

Question 87

Sketch the graph of the polynomial function. -

(Multiple Choice)

4.8/5

(40)

Question 88

Use the intermediate value theorem for polynomials to show that the polynomial function has a real zero between the numbers given. - $f ( x ) = x ^ { 4 } - 9 x ^ { 2 } + 18 ; 1.7$ and $1.8$

(Multiple Choice)

4.9/5

(38)

Question 89

If the average cost per unit C(x) to produce x units of plywood is given by C(x) $C ( x ) = \frac { 900 } { x + 30 }$ , what is the unit cost for 20 units?

(Multiple Choice)

4.8/5

(32)

Question 90

Use synthetic division to perform the division. - $\frac { x ^ { 3 } - x ^ { 2 } + 7 } { x + 2 }$

(Multiple Choice)

4.9/5

(34)

Question 91

Use synthetic division to decide whether the given number k is a zero of the given polynomial function. -k = -1; f(x) = -x4 - 6x2 - x + 4

(True/False)

4.9/5

(31)

Question 92

Use the graph to answer the question. -Find the horizontal and vertical asymptotes of the rational function graphed below.

(Multiple Choice)

4.9/5

(39)

Question 93

Give the equations of any horizontal asymptotes. - $g ( x ) = \frac { x + 3 } { x ^ { 2 } - 2 }$

(Multiple Choice)

4.8/5

(33)

Question 94

Give the equations of any vertical asymptotes. - $h ( x ) = \frac { ( x - 6 ) ( x + 5 ) } { x ^ { 2 } - 1 }$

(Multiple Choice)

4.9/5

(32)

Question 95

Provide an appropriate response. -For what values of a does the quadratic function $f ( x ) = a x ^ { 2 } + 4 x + 5$ have two $x$ -intercepts?

(Multiple Choice)

4.7/5

(28)

Question 96

Find an equation for a rational function with the following asymptotes: vertical asymptotes $x = 8$ and $x = - 6$ , horizontal asymptote $y = 2$

(Essay)

4.8/5

(32)

Question 97

Use the remainder theorem and synthetic division to find f(k). - $k = \frac { 1 } { 2 } ; f ( x ) = - 8 x ^ { 3 } + 16 x ^ { 2 } - 8 x$

(Multiple Choice)

4.9/5

(33)

Question 98

John owns a hot dog stand. He has found that his profit is represented by the equation $P ( x ) = - x ^ { 2 } + 56 x + 72$ with P being profits and x the number of hot dogs sold. How many hot dogs must he sell to earn the most profit?

(Multiple Choice)

4.8/5

(31)

Question 99

Find a polynomial of least degree with only real coefficients and having the given zeros. - $4 + \sqrt { 2 } , 4 - \sqrt { 2 }$ , and 3

(Multiple Choice)

4.8/5

(35)

Question 100

Bob owns a watch repair shop. He has found that the cost of operating his shop is given by $c ( x ) = 2 x ^ { 2 } - 156 x + 88$ , where c is cost and x is the number of watches repaired. How many watches must he repair to have the lowest cost?

What is the domain of the graph?

Give the equation of any oblique asymptotes. - $f ( x ) = \frac { x ^ { 2 } + 3 x + 5 } { x + 6 }$

Graph the polynomial function. Factor first if the expression is not in factored form. - $f(x)=x^{3}+4 x^{2}-x-4$ $Graph the polynomial function. Factor first if the expression is not in factored form. - f(x)=x^{3}+4 x^{2}-x-4$

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary. - $f ( x ) = x ^ { 3 } - 64$

Use synthetic division to perform the division. $\frac { x ^ { 4 } + 625 } { x - 5 }$

Sketch the graph of the polynomial function. -

Use the intermediate value theorem for polynomials to show that the polynomial function has a real zero between the numbers given. - $f ( x ) = x ^ { 4 } - 9 x ^ { 2 } + 18 ; 1.7$ and $1.8$

If the average cost per unit C(x) to produce x units of plywood is given by C(x) $C ( x ) = \frac { 900 } { x + 30 }$ , what is the unit cost for 20 units?

Use synthetic division to perform the division. - $\frac { x ^ { 3 } - x ^ { 2 } + 7 } { x + 2 }$

Use synthetic division to decide whether the given number k is a zero of the given polynomial function. -k = -1; f(x) = -x4 - 6x2 - x + 4

Use the graph to answer the question. -Find the horizontal and vertical asymptotes of the rational function graphed below.

Give the equations of any horizontal asymptotes. - $g ( x ) = \frac { x + 3 } { x ^ { 2 } - 2 }$

Give the equations of any vertical asymptotes. - $h ( x ) = \frac { ( x - 6 ) ( x + 5 ) } { x ^ { 2 } - 1 }$

Provide an appropriate response. -For what values of a does the quadratic function $f ( x ) = a x ^ { 2 } + 4 x + 5$ have two $x$ -intercepts?

Find an equation for a rational function with the following asymptotes: vertical asymptotes $x = 8$ and $x = - 6$ , horizontal asymptote $y = 2$

Use the remainder theorem and synthetic division to find f(k). - $k = \frac { 1 } { 2 } ; f ( x ) = - 8 x ^ { 3 } + 16 x ^ { 2 } - 8 x$

John owns a hot dog stand. He has found that his profit is represented by the equation $P ( x ) = - x ^ { 2 } + 56 x + 72$ with P being profits and x the number of hot dogs sold. How many hot dogs must he sell to earn the most profit?

Find a polynomial of least degree with only real coefficients and having the given zeros. - $4 + \sqrt { 2 } , 4 - \sqrt { 2 }$ , and 3

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Inverse, Exponential, and Logarithmic Functions

Systems and Matrices

Arithmetic Sequence: Common Difference and First n Terms

Filters

Exam 4: Polynomials and Rational Functions

Bob owns a watch repair shop. He has found that the cost of operating his shop is given by c(x)=2x2−156x+88c ( x ) = 2 x ^ { 2 } - 156 x + 88c(x)=2x2−156x+88 , where c is cost and x is the number of watches repaired. How many watches must he repair to have the lowest cost?

What is the domain of the graph?

Give the equation of any oblique asymptotes. - f(x)=x2+3x+5x+6f ( x ) = \frac { x ^ { 2 } + 3 x + 5 } { x + 6 }f(x)=x+6x2+3x+5​

Graph the polynomial function. Factor first if the expression is not in factored form. - f(x)=x3+4x2−x−4f(x)=x^{3}+4 x^{2}-x-4f(x)=x3+4x2−x−4

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary. - f(x)=x3−64f ( x ) = x ^ { 3 } - 64f(x)=x3−64

Use synthetic division to perform the division. x4+625x−5\frac { x ^ { 4 } + 625 } { x - 5 }x−5x4+625​

Sketch the graph of the polynomial function. -

Use the intermediate value theorem for polynomials to show that the polynomial function has a real zero between the numbers given. - f(x)=x4−9x2+18;1.7f ( x ) = x ^ { 4 } - 9 x ^ { 2 } + 18 ; 1.7f(x)=x4−9x2+18;1.7 and 1.81.81.8

If the average cost per unit C(x) to produce x units of plywood is given by C(x) C(x)=900x+30C ( x ) = \frac { 900 } { x + 30 }C(x)=x+30900​ , what is the unit cost for 20 units?

Use synthetic division to perform the division. - x3−x2+7x+2\frac { x ^ { 3 } - x ^ { 2 } + 7 } { x + 2 }x+2x3−x2+7​

Use synthetic division to decide whether the given number k is a zero of the given polynomial function. -k = -1; f(x) = -x4 - 6x2 - x + 4

Use the graph to answer the question. -Find the horizontal and vertical asymptotes of the rational function graphed below.

Give the equations of any horizontal asymptotes. - g(x)=x+3x2−2g ( x ) = \frac { x + 3 } { x ^ { 2 } - 2 }g(x)=x2−2x+3​

Give the equations of any vertical asymptotes. - h(x)=(x−6)(x+5)x2−1h ( x ) = \frac { ( x - 6 ) ( x + 5 ) } { x ^ { 2 } - 1 }h(x)=x2−1(x−6)(x+5)​

Provide an appropriate response. -For what values of a does the quadratic function f(x)=ax2+4x+5f ( x ) = a x ^ { 2 } + 4 x + 5f(x)=ax2+4x+5 have two xxx -intercepts?

Find an equation for a rational function with the following asymptotes: vertical asymptotes x=8x = 8x=8 and x=−6x = - 6x=−6 , horizontal asymptote y=2y = 2y=2

Use the remainder theorem and synthetic division to find f(k). - k=12;f(x)=−8x3+16x2−8xk = \frac { 1 } { 2 } ; f ( x ) = - 8 x ^ { 3 } + 16 x ^ { 2 } - 8 xk=21​;f(x)=−8x3+16x2−8x

John owns a hot dog stand. He has found that his profit is represented by the equation P(x)=−x2+56x+72P ( x ) = - x ^ { 2 } + 56 x + 72P(x)=−x2+56x+72 with P being profits and x the number of hot dogs sold. How many hot dogs must he sell to earn the most profit?

Find a polynomial of least degree with only real coefficients and having the given zeros. - 4+2,4−24 + \sqrt { 2 } , 4 - \sqrt { 2 }4+2​,4−2​ , and 3

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Inverse, Exponential, and Logarithmic Functions

Systems and Matrices

Arithmetic Sequence: Common Difference and First n Terms

Filters

Bob owns a watch repair shop. He has found that the cost of operating his shop is given by $c ( x ) = 2 x ^ { 2 } - 156 x + 88$ , where c is cost and x is the number of watches repaired. How many watches must he repair to have the lowest cost?

Give the equation of any oblique asymptotes. - $f ( x ) = \frac { x ^ { 2 } + 3 x + 5 } { x + 6 }$

Graph the polynomial function. Factor first if the expression is not in factored form. - $f(x)=x^{3}+4 x^{2}-x-4$ $Graph the polynomial function. Factor first if the expression is not in factored form. - f(x)=x^{3}+4 x^{2}-x-4$

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary. - $f ( x ) = x ^ { 3 } - 64$

Use synthetic division to perform the division. $\frac { x ^ { 4 } + 625 } { x - 5 }$

Use the intermediate value theorem for polynomials to show that the polynomial function has a real zero between the numbers given. - $f ( x ) = x ^ { 4 } - 9 x ^ { 2 } + 18 ; 1.7$ and $1.8$

If the average cost per unit C(x) to produce x units of plywood is given by C(x) $C ( x ) = \frac { 900 } { x + 30 }$ , what is the unit cost for 20 units?

Use synthetic division to perform the division. - $\frac { x ^ { 3 } - x ^ { 2 } + 7 } { x + 2 }$

Give the equations of any horizontal asymptotes. - $g ( x ) = \frac { x + 3 } { x ^ { 2 } - 2 }$

Give the equations of any vertical asymptotes. - $h ( x ) = \frac { ( x - 6 ) ( x + 5 ) } { x ^ { 2 } - 1 }$

Provide an appropriate response. -For what values of a does the quadratic function $f ( x ) = a x ^ { 2 } + 4 x + 5$ have two $x$ -intercepts?

Find an equation for a rational function with the following asymptotes: vertical asymptotes $x = 8$ and $x = - 6$ , horizontal asymptote $y = 2$

Use the remainder theorem and synthetic division to find f(k). - $k = \frac { 1 } { 2 } ; f ( x ) = - 8 x ^ { 3 } + 16 x ^ { 2 } - 8 x$

John owns a hot dog stand. He has found that his profit is represented by the equation $P ( x ) = - x ^ { 2 } + 56 x + 72$ with P being profits and x the number of hot dogs sold. How many hot dogs must he sell to earn the most profit?

Find a polynomial of least degree with only real coefficients and having the given zeros. - $4 + \sqrt { 2 } , 4 - \sqrt { 2 }$ , and 3