Question 1

Identify the vertex of the parabola.
-$$f ( x ) = - 7 x ^ { 2 }$$

Accepted Answer

A)  $( 0,0 )$ 
B)  $( - 7,0 )$ 
C)  $( 7,0 )$ 
D)  $( 0 , - 7 )$ 
A)  $( 0,0 )$ 
B)  $( - 7,0 )$ 
C)  $( 7,0 )$ 
D)  $( 0 , - 7 )$

Question 2

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions.
-Zeros of $- 3,2,6$ and $\mathrm { P } ( 1 ) = 20$

Accepted Answer

A)  $P ( x ) = x ^ { 3 } - 5 x ^ { 2 } - 12 x + 36$ 
B)  $P ( x ) = x ^ { 3 } - 5 x ^ { 2 } - 11 x + 30$ 
C)  $P ( x ) = x ^ { 3 } - 5 x ^ { 2 } - 12 x - 36$ 
D)  $P ( x ) = x ^ { 3 } + 5 x ^ { 2 } - 11 x + 30$ 
A)  $P ( x ) = x ^ { 3 } - 5 x ^ { 2 } - 12 x + 36$ 
B)  $P ( x ) = x ^ { 3 } - 5 x ^ { 2 } - 11 x + 30$ 
C)  $P ( x ) = x ^ { 3 } - 5 x ^ { 2 } - 12 x - 36$ 
D)  $P ( x ) = x ^ { 3 } + 5 x ^ { 2 } - 11 x + 30$

Question 3

The student population of a small school has been increasing as shown in the following table.

Take 1910 as year zero, and determine the linear or quadratic function that best fits the data.

Accepted Answer

A)  $f ( x ) = 0.16 x ^ { 2 } - 17.5 x + 106$ 
B)  $f ( x ) = 0.27 x ^ { 2 } - 29.1 x - 410$ 
C)  $f ( x ) = 0.1 x ^ { 2 } - 10 x + 440$ 
D)  $f ( x ) = 5 x - 93.2$ 
A)  $f ( x ) = 0.16 x ^ { 2 } - 17.5 x + 106$ 
B)  $f ( x ) = 0.27 x ^ { 2 } - 29.1 x - 410$ 
C)  $f ( x ) = 0.1 x ^ { 2 } - 10 x + 440$ 
D)  $f ( x ) = 5 x - 93.2$

Question 4

Find the equation of the axis of symmetry of the parabola.
$y = x ^ { 2 } - 10 x + 26$

Accepted Answer

A)   x=5 
B)   x=-5 
C)   x=0 
D)   x=1 
A)   x=5 
B)   x=-5 
C)   x=0 
D)   x=1

Question 5

Match the equation to the correct graph
$y = - ( x + 2 ) ^ { 2 } + 2$

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 6

Find the domain and range of the function.
-$$f ( x ) = ( x - 2 ) ^ { 2 } + 2$$

Accepted Answer

A)  Domain: $( - 2 , \infty )$; range: $( - \infty , \infty )$ 
B)  Domain: $( - \infty , \infty )$; range: $[ 2 , \infty )$ 
C)  Domain: $( - \infty , \infty )$; range: $( - \infty , 2 )$ 
D)  Domain: $( - \infty , 2 )$; range: $( - \infty , \infty )$ 
A)  Domain: $( - 2 , \infty )$; range: $( - \infty , \infty )$ 
B)  Domain: $( - \infty , \infty )$; range: $[ 2 , \infty )$ 
C)  Domain: $( - \infty , \infty )$; range: $( - \infty , 2 )$ 
D)  Domain: $( - \infty , 2 )$; range: $( - \infty , \infty )$

Question 7

Use Descartes' Rule of Signs to determine the possible number of positive real zeros and the possible number of negative real zeros for the function.
-
f ( x ) = 9 x ^ { 6 } - 8 x ^ { 4 } - 3 x ^ { 3 } + 9 x ^ { 2 } - 8 x

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 8

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary.
-$$f ( x ) = x ^ { 3 } - 7 x ^ { 2 } + 15 x - 25$$

Accepted Answer

A)  $5,1 + 2 \mathrm { i } , 1 - 2 \mathrm { i }$ 
B)  $5 , - 1 + 2 \mathrm { i } , - 1 - 2 \mathrm { i }$ 
C)  $5,1 + \sqrt { 5 } , 1 - \sqrt { 5 }$ 
D)  $5,1 + \sqrt { 5 } i , 1 - \sqrt { 5 } i$ 
A)  $5,1 + 2 \mathrm { i } , 1 - 2 \mathrm { i }$ 
B)  $5 , - 1 + 2 \mathrm { i } , - 1 - 2 \mathrm { i }$ 
C)  $5,1 + \sqrt { 5 } , 1 - \sqrt { 5 }$ 
D)  $5,1 + \sqrt { 5 } i , 1 - \sqrt { 5 } i$

Question 9

Factor f(x) into linear factors given that k is a zero of f(x).
-$$f ( x ) = x ^ { 3 } - 4 x ^ { 2 } - 25 x + 100 ; k = 5$$

Accepted Answer

A)  $( x - 5 ) ( x + 4 ) ( x + 5 )$ 
B)  $x ( x - 5 ) ( x - 4 )$ 
C)  $( x - 5 ) ( x - 4 ) ( x + 5 )$ 
D)  $( x - 5 ) ( x - 4 ) ( x + 4 )$ 
A)  $( x - 5 ) ( x + 4 ) ( x + 5 )$ 
B)  $x ( x - 5 ) ( x - 4 )$ 
C)  $( x - 5 ) ( x - 4 ) ( x + 5 )$ 
D)  $( x - 5 ) ( x - 4 ) ( x + 4 )$

Question 10

Find the equation of the axis of symmetry of the parabola.
$y = 3 x ^ { 2 } + 30 x + 74$

Accepted Answer

A)   x=-1 
B)   x=-5 
C)   x=1 
D)   x=5 
A)   x=-1 
B)   x=-5 
C)   x=1 
D)   x=5

Question 11

A plane suddenly experiences turbulence while in flight. At this point the change in its altitude, in feet, is represented by the following function of time: $F ( x ) = \frac { 4 ( x - 8 ) ^ { 2 } - 6 } { 16 ( x - 8 ) ^ { 2 } - 8 ( x - 8 ) + 12 }$. Assuming that the turbulence first hits at time $x = 0$, what is the maximum relative drop the plane will experience due to turbulence? (Round the result to the nearest hundredth.)

Accepted Answer

A)  0.53 ft 
B)  0.26 ft 
C)  16.83 ft 
D)  8.17 ft 
A)  0.53 ft 
B)  0.26 ft 
C)  16.83 ft 
D)  8.17 ft

Question 12

If f varies jointly as $\mathrm { q } ^ { 2 }$ and  h, and f=144  when q=4  and h=3 , find  q when  f=72  and h=6 .

Accepted Answer

A)  6 
B)  2 
C)  3 
D)  4 
A)  6 
B)  2 
C)  3 
D)  4

Question 13

Round to the nearest tenth unless indicated otherwise.
-The resistance of a wire varies directly as the length of the wire and inversely as the square of the diameter of the wire. A 20 foot length of wire with a diameter of 0.1 inch has a resistance of 3 ohms. What would the
Resistance be for a 25 foot length, with diameter 0.01 inch, of the same kind of wire ?

Accepted Answer

A)  368 ohms 
B)  372.5 ohms 
C)  375 ohms 
D)  387 ohms 
A)  368 ohms 
B)  372.5 ohms 
C)  375 ohms 
D)  387 ohms

Question 14

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions.
Zeros of  -5  and  1 - i, P(0)=10

Accepted Answer

A)  $P ( x ) = x ^ { 3 } + 3 x ^ { 2 } - 8 x$ 
B)  $P ( x ) = x ^ { 3 } + 3 x ^ { 2 } - 8 x + 10$ 
C)  $P ( x ) = x ^ { 3 } + 3 x ^ { 2 } + 8 x + 10$ 
D)  $P ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 3 x + 5$ 
A)  $P ( x ) = x ^ { 3 } + 3 x ^ { 2 } - 8 x$ 
B)  $P ( x ) = x ^ { 3 } + 3 x ^ { 2 } - 8 x + 10$ 
C)  $P ( x ) = x ^ { 3 } + 3 x ^ { 2 } + 8 x + 10$ 
D)  $P ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 3 x + 5$

Question 15

The polynomial function $I ( t ) = - 0.1 t ^ { 2 } + 1.9$ t represents the yearly income (or loss) from a real estate investment, where t is time in years. After what year does income begin to decline?

Accepted Answer

A)  19 yr 
B)  9.5 yr 
C)  8.5 yr 
D)  12.67 yr 
A)  19 yr 
B)  9.5 yr 
C)  8.5 yr 
D)  12.67 yr

Question 16

Tell whether a linear model or a quadratic model is appropriate for the data. If linear, tell whether the slope should be positive or negative. If quadratic, decide whether the leading coefficient a of $x ^ { 2 }$ should be positive or negative.
-The amount of sales tax paid as a function of the sales price.

Accepted Answer

A)  quadratic; negative 
B)  linear; positive 
C)  linear; negative 
D)  quadratic; positive 
A)  quadratic; negative 
B)  linear; positive 
C)  linear; negative 
D)  quadratic; positive

Question 17

Use synthetic division to decide whether the given number k is a zero of the given polynomial function.
-$k = 2 + 2 i ; f ( x ) = x ^ { 2 } - 4 x + 8$

Accepted Answer

A) True 
 B)False

Question 18

Sketch the graph of the rational function.
-$$f ( x ) = \frac { x - 3 } { x + 4 }$$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 19

Use the factor theorem to decide whether or not the second polynomial is a factor of the first.
-$- 8 x ^ { 3 } + 30 x ^ { 2 } - 7 x + 4 ; x + 4$

Accepted Answer

A) True 
 B)False

Question 20

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions.
Zeros of 5 and i,P(1)=-8

Accepted Answer

A)  $P ( x ) = x ^ { 3 } - 5 x ^ { 2 } + x + 5$ 
B)  $P ( x ) = x ^ { 3 } + 5 x ^ { 2 } - x + 5$ 
C)  $P ( x ) = x ^ { 3 } - 5 x ^ { 2 } + x - 5$ 
D)  $P ( x ) = x ^ { 3 } + 5 x ^ { 2 } + x - 5$ 
A)  $P ( x ) = x ^ { 3 } - 5 x ^ { 2 } + x + 5$ 
B)  $P ( x ) = x ^ { 3 } + 5 x ^ { 2 } - x + 5$ 
C)  $P ( x ) = x ^ { 3 } - 5 x ^ { 2 } + x - 5$ 
D)  $P ( x ) = x ^ { 3 } + 5 x ^ { 2 } + x - 5$

Identify the vertex of the parabola. - $f ( x ) = - 7 x ^ { 2 }$

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions. -Zeros of $- 3,2,6$ and $\mathrm { P } ( 1 ) = 20$

The student population of a small school has been increasing as shown in the following table. Take 1910 as year zero, and determine the linear or quadratic function that best fits the data.

Find the equation of the axis of symmetry of the parabola. $y = x ^ { 2 } - 10 x + 26$

Match the equation to the correct graph $y = - ( x + 2 ) ^ { 2 } + 2$

Find the domain and range of the function. - $f ( x ) = ( x - 2 ) ^ { 2 } + 2$

Use Descartes' Rule of Signs to determine the possible number of positive real zeros and the possible number of negative real zeros for the function. - f ( x ) = 9 x ^ { 6 } - 8 x ^ { 4 } - 3 x ^ { 3 } + 9 x ^ { 2 } - 8 x

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary. - $f ( x ) = x ^ { 3 } - 7 x ^ { 2 } + 15 x - 25$

Factor f(x) into linear factors given that k is a zero of f(x). - $f ( x ) = x ^ { 3 } - 4 x ^ { 2 } - 25 x + 100 ; k = 5$

Find the equation of the axis of symmetry of the parabola. $y = 3 x ^ { 2 } + 30 x + 74$

If f varies jointly as $\mathrm { q } ^ { 2 }$ and h, and f=144 when q=4 and h=3 , find q when f=72 and h=6 .

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions. Zeros of -5 and 1 - i, P(0)=10

The polynomial function $I ( t ) = - 0.1 t ^ { 2 } + 1.9$ t represents the yearly income (or loss) from a real estate investment, where t is time in years. After what year does income begin to decline?

Use synthetic division to decide whether the given number k is a zero of the given polynomial function. - $k = 2 + 2 i ; f ( x ) = x ^ { 2 } - 4 x + 8$

Sketch the graph of the rational function. - $f ( x ) = \frac { x - 3 } { x + 4 }$ $Sketch the graph of the rational function. - f ( x ) = \frac { x - 3 } { x + 4 }$

Use the factor theorem to decide whether or not the second polynomial is a factor of the first. - $- 8 x ^ { 3 } + 30 x ^ { 2 } - 7 x + 4 ; x + 4$

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions. Zeros of 5 and i,P(1)=-8

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

Identify the vertex of the parabola. - f(x)=−7x2f ( x ) = - 7 x ^ { 2 }f(x)=−7x2

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions. -Zeros of −3,2,6- 3,2,6−3,2,6 and P(1)=20\mathrm { P } ( 1 ) = 20P(1)=20

The student population of a small school has been increasing as shown in the following table. Take 1910 as year zero, and determine the linear or quadratic function that best fits the data.

Find the equation of the axis of symmetry of the parabola. y=x2−10x+26y = x ^ { 2 } - 10 x + 26y=x2−10x+26

Match the equation to the correct graph y=−(x+2)2+2y = - ( x + 2 ) ^ { 2 } + 2y=−(x+2)2+2

Find the domain and range of the function. - f(x)=(x−2)2+2f ( x ) = ( x - 2 ) ^ { 2 } + 2f(x)=(x−2)2+2

Use Descartes' Rule of Signs to determine the possible number of positive real zeros and the possible number of negative real zeros for the function. - f ( x ) = 9 x ^ { 6 } - 8 x ^ { 4 } - 3 x ^ { 3 } + 9 x ^ { 2 } - 8 x

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary. - f(x)=x3−7x2+15x−25f ( x ) = x ^ { 3 } - 7 x ^ { 2 } + 15 x - 25f(x)=x3−7x2+15x−25

Factor f(x) into linear factors given that k is a zero of f(x). - f(x)=x3−4x2−25x+100;k=5f ( x ) = x ^ { 3 } - 4 x ^ { 2 } - 25 x + 100 ; k = 5f(x)=x3−4x2−25x+100;k=5

Find the equation of the axis of symmetry of the parabola. y=3x2+30x+74y = 3 x ^ { 2 } + 30 x + 74y=3x2+30x+74

If f varies jointly as q2\mathrm { q } ^ { 2 }q2 and h, and f=144 when q=4 and h=3 , find q when f=72 and h=6 .

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions. Zeros of -5 and 1 - i, P(0)=10

The polynomial function I(t)=−0.1t2+1.9I ( t ) = - 0.1 t ^ { 2 } + 1.9I(t)=−0.1t2+1.9 t represents the yearly income (or loss) from a real estate investment, where t is time in years. After what year does income begin to decline?

Use synthetic division to decide whether the given number k is a zero of the given polynomial function. - k=2+2i;f(x)=x2−4x+8k = 2 + 2 i ; f ( x ) = x ^ { 2 } - 4 x + 8k=2+2i;f(x)=x2−4x+8

Sketch the graph of the rational function. - f(x)=x−3x+4f ( x ) = \frac { x - 3 } { x + 4 }f(x)=x+4x−3​

Use the factor theorem to decide whether or not the second polynomial is a factor of the first. - −8x3+30x2−7x+4;x+4- 8 x ^ { 3 } + 30 x ^ { 2 } - 7 x + 4 ; x + 4−8x3+30x2−7x+4;x+4

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions. Zeros of 5 and i,P(1)=-8

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

Identify the vertex of the parabola. - $f ( x ) = - 7 x ^ { 2 }$

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions. -Zeros of $- 3,2,6$ and $\mathrm { P } ( 1 ) = 20$

Find the equation of the axis of symmetry of the parabola. $y = x ^ { 2 } - 10 x + 26$

Match the equation to the correct graph $y = - ( x + 2 ) ^ { 2 } + 2$

Find the domain and range of the function. - $f ( x ) = ( x - 2 ) ^ { 2 } + 2$

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary. - $f ( x ) = x ^ { 3 } - 7 x ^ { 2 } + 15 x - 25$

Factor f(x) into linear factors given that k is a zero of f(x). - $f ( x ) = x ^ { 3 } - 4 x ^ { 2 } - 25 x + 100 ; k = 5$

Find the equation of the axis of symmetry of the parabola. $y = 3 x ^ { 2 } + 30 x + 74$

If f varies jointly as $\mathrm { q } ^ { 2 }$ and h, and f=144 when q=4 and h=3 , find q when f=72 and h=6 .

The polynomial function $I ( t ) = - 0.1 t ^ { 2 } + 1.9$ t represents the yearly income (or loss) from a real estate investment, where t is time in years. After what year does income begin to decline?

Use synthetic division to decide whether the given number k is a zero of the given polynomial function. - $k = 2 + 2 i ; f ( x ) = x ^ { 2 } - 4 x + 8$

Sketch the graph of the rational function. - $f ( x ) = \frac { x - 3 } { x + 4 }$ $Sketch the graph of the rational function. - f ( x ) = \frac { x - 3 } { x + 4 }$

Use the factor theorem to decide whether or not the second polynomial is a factor of the first. - $- 8 x ^ { 3 } + 30 x ^ { 2 } - 7 x + 4 ; x + 4$