Section 4.1 Question: Find the vertex of the parabola y  =  –3x2 – 6x – 1. Write your answer as an ordered pair (x, y).
 
Quiz 5.6    

Section 4.2
Quiz 5.7
Question: For the polynomial (x + 6)2(x – 6), list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at each x-intercept.
 
    –6, multiplicity 1, crosses the x-axis; 6, multiplicity 2, touches the x-axis
6, multiplicity 1, touches the x-axis; –6, multiplicity 2, crosses the x-axis
6, multiplicity 1, crosses the x-axis; –6, multiplicity 2, touches the x-axis
–6, multiplicity 1, touches the x-axis; 6, multiplicity 2, crosses the x-axis
 
  Variation: For the polynomial –3(x + 1)(x – 1)2, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at each x-intercept.
 
    1, multiplicity 1, touches the x-axis; –1, multiplicity 2, crosses the x-axis
–1, multiplicity 1, crosses the x-axis; 1, multiplicity 2, touches the x-axis
–1, multiplicity 1, touches the x-axis; 1, multiplicity 2, crosses the x-axis
1, multiplicity 1, crosses the x-axis; –1, multiplicity 2, touches the x-axis
 

Section 4.2
Quiz 5.8
Question: Give the possible values for the degree of the polynomial and the sign (+ or –) of the leading coefficient (xn term).

 
    Degree is odd (1, 3, 5, etc.); leading coefficient is positive.
Degree is odd (1, 3, 5, etc.); leading coefficient is negative.
Degree is even (2, 4, 6, etc.); leading coefficient is positive.
Degree is even (2, 4, 6, etc.); leading coefficient is negative.
 
  Variations: Give the possible values for the degree of the polynomial and the sign (+ or –) of the leading coefficient (xn term).

 
    Give the possible values for the degree of the polynomial and the sign (+ or –) of the leading coefficient (xn term).

 
    Give the possible values for the degree of the polynomial and the sign (+ or –) of the leading coefficient (xn term).

 

Section 4.3
Quiz 6.1
Question: Identify the vertical asymptotes for the following function:
f (x)  =   x – 7
x2 + x

 
    x = –1
x = 0
none
x = –7
x = –1, x = 0
x = 7
x = 1
x = 0, x = 1
 
  Variations: Identify the vertical asymptotes for the following function:
f (x)  =   x + 4
x2x

 
    x = 0, x = 1
x = –1
x = –1, x = 0
x = 1
x = 0
x = 4
none
x = –4
 
    Identify the vertical asymptotes for the following function:
f (x)  =   x + 5
x2 + 4

 
    x = –5
x = –2
x = 5
x = 2
none
x = –2, x = 2
 
    Identify the vertical asymptotes for the following function:
f (x)  =   x – 6
x2 – 1

 
    x = –1, x = 1
x = –6
x = –1
x = 1
none
x = 6
 

Section 4.3
Quiz 6.2
Question: Write the equation for the horizontal or oblique asymptote of the following function. If there is no horizontal or oblique asymptote, enter none
6x3 – 5x2 – 5
2x2x + 7

 
     
  Variations: Write the equation for the horizontal or oblique asymptote of the following function. If there is no horizontal or oblique asymptote, enter none
–6x2 + 7x + 7
2x2x – 7

 
     
    Write the equation for the horizontal or oblique asymptote of the following function. If there is no horizontal or oblique asymptote, enter none
–6x2x + 7
2x3x2 – 5

 
     
    Write the equation for the horizontal or oblique asymptote of the following function. If there is no horizontal or oblique asymptote, enter none
–6x4x3 + 7
2x2x – 5

 
     

Question 5   Fill in the Blank (1 points)
Section 4.5
Quiz 6.3
Question: Solve the following inequality. You may express your answer as an inequality or you may use interval notation. Write an inequality like 2  <  x  ≤ 5 OR x  ≥  8 as 2<x<=5 or x>=8. Write a solution composed of two intervals like x is in (–∞, 2] or x is in (5, 8] as (-infinity,2] or (5,8].
x
(x + 4)(x + 1)
   ≤  0

 
     
  Variation: Solve the following inequality. You may express your answer as an inequality or you may use interval notation. Write an inequality like 2  <  x  ≤ 5 OR x  ≥  8 as 2<x<=5 or x>=8. Write a solution composed of two intervals like x is in (–∞, 2] or x is in (5, 8] as (-infinity,2] or (5,8].
x(x + 4)
x + 1
   ≥  0

 
     

Section 4.5
Quiz 6.4
Question: Solve the following inequality. You may express your answer as an inequality or you may use interval notation. Write an inequality like 2 < x ≤5 OR x ≥ 8 as 2<x<=5 or x>=8. Write a solution composed of two intervals like x is in (–∞, 2] or x is in (5, 8] as (-infinity,2] or (5,8].
x (x – 3)3  >  0

 
     
  Variation: Solve the following inequality. You may express your answer as an inequality or you may use interval notation. Write an inequality like 2 < x ≤5 OR x ≥ 8 as 2<x<=5 or x>=8. Write a solution composed of two intervals like x is in (–∞, 2] or x is in (5, 8] as (-infinity,2] or (5,8].
(x – 1) (x – 3)3  ≤  0

 
     
    Solve the following inequality. You may express your answer as an inequality or you may use interval notation. Write an inequality like 2 < x ≤5 OR x ≥ 8 as 2<x<=5 or x>=8. Write a solution composed of two intervals like x is in (–∞, 2] or x is in (5, 8] as (-infinity,2] or (5,8].
(x – 1) (x – 3)2  ≥  0

 
     
    Solve the following inequality. You may express your answer as an inequality or you may use interval notation. Write an inequality like 2 < x ≤5 OR x ≥ 8 as 2<x<=5 or x>=8. Write a solution composed of two intervals like x is in (–∞, 2] or x is in (5, 8] as (-infinity,2] or (5,8].
x (x – 3)2  ≤  0

 
     
    Solve the following inequality. You may express your answer as an inequality or you may use interval notation. Write an inequality like 2 < x ≤5 OR x ≥ 8 as 2<x<=5 or x>=8. Write a solution composed of two intervals like x is in (–∞, 2] or x is in (5, 8] as (-infinity,2] or (5,8].
(x – 3) (x – 1)2  >  0

 
     
    Solve the following inequality. You may express your answer as an inequality or you may use interval notation. Write an inequality like 2 < x ≤5 OR x ≥ 8 as 2<x<=5 or x>=8. Write a solution composed of two intervals like x is in (–∞, 2] or x is in (5, 8] as (-infinity,2] or (5,8].
(x – 1) x2  <  0