Question 1

Find the vertex, focus, and directrix for the given parabola.

Accepted Answer

A)  Vertex: (6, 7); Focus: (-6, 5); Directrix: y = 5 
B)  Vertex: (6, 7); Focus: (-6, 9); Directrix: y = 9 
C)  Vertex: (-6, 7); Focus: (-6, 9); Directrix: y = 5 
D)  Vertex: (-6, 7); Focus: (-6, 5); Directrix: y = 9 
A)  Vertex: (6, 7); Focus: (-6, 5); Directrix: y = 5 
B)  Vertex: (6, 7); Focus: (-6, 9); Directrix: y = 9 
C)  Vertex: (-6, 7); Focus: (-6, 9); Directrix: y = 5 
D)  Vertex: (-6, 7); Focus: (-6, 5); Directrix: y = 9 C

Question 2

Write the standard equation for the circle with the given radius and center. Center (-10, -2), radius 5

Accepted Answer

A)  (x - 10)2 + (y - 2)2 = 25 
B)  (x - 10)2 + (y - 2)2 = 5 
C)  (x + 10)2 + (y + 2)2 = 5 
D)  (x + 10)2 + (y + 2)2 = 25 
A)  (x - 10)2 + (y - 2)2 = 25 
B)  (x - 10)2 + (y - 2)2 = 5 
C)  (x + 10)2 + (y + 2)2 = 5 
D)  (x + 10)2 + (y + 2)2 = 25 D

Question 3

Find the midpoint and length of the line segment with the endpoints (2,3) and (5,8).

Accepted Answer

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

Question 4

Find the distance between (-5, -4) and (-7, -3).

Accepted Answer

A)    
B)  2 
C)    
D)    
A)    
B)  2 
C)    
D)

Question 5

Which of the following is the correct graph of   ?

Accepted Answer

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

Question 6

Solve the given system of equations. xy = 10
Y = x

Accepted Answer

A)  Ø 
B) 
  
C)  {(-10, -10), (0, 0), (10, 10)} 
D)  {(0, 10), (10, 0)} 
A)  Ø 
B) 
  
C)  {(-10, -10), (0, 0), (10, 10)} 
D)  {(0, 10), (10, 0)}

Question 7

Which of the following is the correct graph of   ?

Accepted Answer

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

Question 8

Determine which equation has a graph which is an ellipse.

Accepted Answer

A)  9x2 - y2 = 1 
B)    
C)  x2 + 9y = 1 
D)  x2 + y2 = 9 
A)  9x2 - y2 = 1 
B)    
C)  x2 + 9y = 1 
D)  x2 + y2 = 9

Question 9

Determine which equation has a graph which is a circle.

Accepted Answer

A)  4x2 - y2 = 1 
B)    
C)  x2 + 4y = 1 
D)  x2 + y2 = 4 
A)  4x2 - y2 = 1 
B)    
C)  x2 + 4y = 1 
D)  x2 + y2 = 4

Question 10

Solve the system by elimination.

Accepted Answer

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

Question 11

Solve the given system of equations. y = x2 - 10
5x + y = 4

Accepted Answer

A)  {(2, 14), (-7, 59)} 
B)  {(2, -6), (-7, 39)} 
C)  {(2, 4), (-7, 49)} 
D)  {(2, -6), (-7, 49)} 
A)  {(2, 14), (-7, 59)} 
B)  {(2, -6), (-7, 39)} 
C)  {(2, 4), (-7, 49)} 
D)  {(2, -6), (-7, 49)}

Question 12

Which of the following is the correct graph of   ?

Accepted Answer

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

Question 13

Determine which equation has a graph which is a parabola.

Accepted Answer

A)  x2 + 16y = 1 
B)    
C)  x2 + y2 = 16 
D)  16x2 - y2 = 1 
A)  x2 + 16y = 1 
B)    
C)  x2 + y2 = 16 
D)  16x2 - y2 = 1

Question 14

Find the lengths of the legs of a right triangle whose hypotenuse is   and whose area is 15 square inches.

Accepted Answer

A) 
  feet and
  feet 
B) 
  feet and
  feet 
C) 
  feet and
  feet 
D) 
  feet and
  feet 
A) 
  feet and
  feet 
B) 
  feet and
  feet 
C) 
  feet and
  feet 
D) 
  feet and
  feet

Question 15

Rewrite the given equation in the standard form for the equation of a circle and identify its center and radius. x2 - 2x + y2 + 2y - 98 = 0

Accepted Answer

A)  (x + 1)2 + (y - 1)2 = 10; (-1, 1); 10 
B)  (x - 1)2 + (y + 1)2 = 10; (1, -1); 10 
C)  (x - 1)2 + (y + 1)2 = 100; (1, -1); 10 
D)  (x + 1)2 + (y - 1)2 = 100; (-1, 1); 10 
A)  (x + 1)2 + (y - 1)2 = 10; (-1, 1); 10 
B)  (x - 1)2 + (y + 1)2 = 10; (1, -1); 10 
C)  (x - 1)2 + (y + 1)2 = 100; (1, -1); 10 
D)  (x + 1)2 + (y - 1)2 = 100; (-1, 1); 10

Question 16

Which of the following is the correct graph of   ?

Accepted Answer

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

Question 17

Determine whether the graph of the equation is a circle, parabola, ellipse, or hyperbola. (x + 8)2 - y = 1

Accepted Answer

A)  Ellipse 
B)  Circle 
C)  Hyperbola 
D)  Parabola 
A)  Ellipse 
B)  Circle 
C)  Hyperbola 
D)  Parabola

Question 18

Graph both equations of the system on the same coordinate axes. Use elimination to find all points of intersection. y = x2 - 4
X2 + 4y2 = 4

Accepted Answer

A)  (0, -1), (-2, 0), (2, 0)
  
B)  (0, 1), (-2, 0), (2, 0)
  
C)  (-2, 0), (2, 0)
  
D)  (-2, 0), (2, 0)
  
A)  (0, -1), (-2, 0), (2, 0)
  
B)  (0, 1), (-2, 0), (2, 0)
  
C)  (-2, 0), (2, 0)
  
D)  (-2, 0), (2, 0)

Question 19

Find the equation of the parabola with the given focus and directrix. Focus: (3, 0); Directrix: y = -4

Accepted Answer

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

Question 20

Which of the following graphs correctly represents the solution set for the given system of inequalities?

Accepted Answer

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

Exam 13: Section 1: Nonlinear Systems and the Conic Sections

Find the vertex, focus, and directrix for the given parabola.

Write the standard equation for the circle with the given radius and center. Center (-10, -2), radius 5

Find the midpoint and length of the line segment with the endpoints (2,3) and (5,8).

Find the distance between (-5, -4) and (-7, -3).

Which of the following is the correct graph of ?

Solve the given system of equations. xy = 10 Y = x

Which of the following is the correct graph of ?

Determine which equation has a graph which is an ellipse.

Determine which equation has a graph which is a circle.

Solve the system by elimination.

Solve the given system of equations. y = x2 - 10 5x + y = 4

Which of the following is the correct graph of ?

Determine which equation has a graph which is a parabola.

Find the lengths of the legs of a right triangle whose hypotenuse is and whose area is 15 square inches.

Rewrite the given equation in the standard form for the equation of a circle and identify its center and radius. x2 - 2x + y2 + 2y - 98 = 0

Which of the following is the correct graph of ?

Determine whether the graph of the equation is a circle, parabola, ellipse, or hyperbola. (x + 8)2 - y = 1

Graph both equations of the system on the same coordinate axes. Use elimination to find all points of intersection. y = x2 - 4 X2 + 4y2 = 4

Find the equation of the parabola with the given focus and directrix. Focus: (3, 0); Directrix: y = -4

Which of the following graphs correctly represents the solution set for the given system of inequalities?

Section 1: Real Numbers and Their Properties

Section 2: Real Numbers and Their Properties

Section 1: Linear Equations and Inequalities in One Variable

Section 2: Linear Equations and Inequalities in One Variable

Section 1: Linear Equations and Inequalities in Two Variables

Section 2: Linear Equations and Inequalities in Two Variables

Section 1: Exponents and Polynomials

Section 2: Exponents and Polynomials

Section 1: Factoring

Section 2: Factoring

Section 1: Rational Expressions

Section 2: Rational Expressions

Section 1: Systems of Linear Equations

Section 2: Systems of Linear Equations

Section 1: More on Inequalities

Section 2: More on Inequalities

Section 1: Radicals and Rational Exponents

Section 2: Radicals and Rational Exponents

Section 1: Quadratic Equations and Inequalities

Section 2: Quadratic Equations and Inequalities

Section 1: Functions

Section 2: Functions

Section 1: Exponential and Logarithmic Functions

Section 2: Exponential and Logarithmic Functions

Section 2: Nonlinear Systems and the Conic Sections

Section 1: Sequences and Series Available Online at Www.mhhe.com/dugopolski

Section 2: Sequences and Series Available Online at Www.mhhe.com/dugopolski

Mathematical Problem Set

Algebraic Equations and Problem Solving

Algebra and Math Problems

Algebraic Equation Practice

Filters

Solve the given system of equations. y = x² - 10 5x + y = 4

Rewrite the given equation in the standard form for the equation of a circle and identify its center and radius. x² - 2x + y² + 2y - 98 = 0

Determine whether the graph of the equation is a circle, parabola, ellipse, or hyperbola. (x + 8)² - y = 1

Graph both equations of the system on the same coordinate axes. Use elimination to find all points of intersection. y = x² - 4 X² + 4y² = 4