Question 1

Determine the vertex and axis of symmetry for  .

Accepted Answer

A)  vertex:  ; axis:  
B)  vertex:  ; axis:  
C)  vertex:  ; axis:  
D)  vertex:  ; axis:

Question 2

Use the discriminant to determine what type of solutions exist for the quadratic equation. Do not solve the equation.

Accepted Answer

A)  nonreal complex numbers, complex conjugates 
B)  rational, unequal 
C)  irrational, unequal 
D)  rational, equal 
E)  irrational, equal

Question 3

The area of a circle is numerically equal to 8 times the circumference of the circle. Find the length of a radius of the circle.

Accepted Answer

A)  16  
B)  17 
C)  16 
D)  15  
E)  8

Question 4

Use the method of completing the square to solve the quadratic equation.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 5

Write  in terms of i and simplify.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 6

Solve the equation. Enter all roots in bi or a + bi form.

Accepted Answer

A)   
B)   
C)   
D)

Question 7

The cannonball in the illustration follows the parabolic trajectory  . How far short of the castle does it land?

Accepted Answer

A)  5 ft 
B)  6 ft 
C)  3 ft 
D)  4 ft 
E)  2 ft

Question 8

Use the quadratic formula to find all real solutions of the equation.

Accepted Answer

A)   
B)   
C)   
D)   
E)  no real solutions

Question 9

Complete the square and factor the resulting perfect-square trinomial.

Accepted Answer

A)  ( t + 16 )  
B)  ( t - 4 )  
C)  ( t + 4 )  
D)  ( t - 16 )

Question 10

Write the expression in  form.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 11

Write the expression in a + bi form.

Accepted Answer

A)   
B)   
C)   
D)

Question 12

Use the discriminant to determine what type of solutions exist for the quadratic equation. Do not solve the equation.

Accepted Answer

A)  rational, equal 
B)  irrational, unequal 
C)  irrational, equal 
D)  nonreal complex numbers, complex conjugates 
E)  rational, unequal

Question 13

Construct a table of solutions and graph of  .

Accepted Answer

A)     
B)     
C)     
D)

Question 14

A wholesaler sells CD players for $170 each. However, she gives volume discounts on purchases of 100 to 1,500 units according to the formula  , where n represents the number of units purchased. How many units would a retailer have to buy for the wholesaler to obtain maximum revenue?

Accepted Answer

A)  1,170 units 
B)  850 units 
C)  470 units 
D)  550 units 
E)  450 units

Question 15

If the orbit of the comet is approximated by the equation  , how far is it from the sun at the vertex of the orbit? Distances are measured in astronomical units (AU).

Accepted Answer

A)  2 AU 
B)  4 AU 
C)  1 AU 
D)  5 AU 
E)  3 AU

Question 16

Use the square root method to solve the equation.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 17

Write the expression in a + bi form.

Accepted Answer

A)   
B)   
C)   
D)

Question 18

Solve the equation by completing the square.

Accepted Answer

A)   ,  
B)   ,  
C)   ,  
D)   ,  
E)   ,

Question 19

Find the vertex of the graph of the equation. Do not draw the graph.

Accepted Answer

A)   
B)   
C)   
D)

Question 20

Solve the following quadratic equation.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Exam 9: Quadratic Equations, Quadratic Functions, and Complex Numbers

Determine the vertex and axis of symmetry for .

Use the discriminant to determine what type of solutions exist for the quadratic equation. Do not solve the equation.

The area of a circle is numerically equal to 8 times the circumference of the circle. Find the length of a radius of the circle.

Use the method of completing the square to solve the quadratic equation.

Write in terms of i and simplify.

Solve the equation. Enter all roots in bi or a + bi form.

The cannonball in the illustration follows the parabolic trajectory . How far short of the castle does it land?

Use the quadratic formula to find all real solutions of the equation.

Complete the square and factor the resulting perfect-square trinomial.

Write the expression in form.

Write the expression in a + bi form.

Use the discriminant to determine what type of solutions exist for the quadratic equation. Do not solve the equation.

Construct a table of solutions and graph of .

A wholesaler sells CD players for $170 each. However, she gives volume discounts on purchases of 100 to 1,500 units according to the formula , where n represents the number of units purchased. How many units would a retailer have to buy for the wholesaler to obtain maximum revenue?

If the orbit of the comet is approximated by the equation , how far is it from the sun at the vertex of the orbit? Distances are measured in astronomical units (AU) .

Use the square root method to solve the equation.

Write the expression in a + bi form.

Solve the equation by completing the square.

Find the vertex of the graph of the equation. Do not draw the graph.

Solve the following quadratic equation.