Question 1

Solve the inequality. Write the solution set in interval notation.
-$$\frac { x } { x + 3 } > 0$$

Accepted Answer

A)  $( - \infty , - 3 ] \cup [ 0 , \infty )$ 
B)  $( 0 , \infty )$ 
C)  $( - \infty , - 3 ) \cup ( 0 , \infty )$ 
D)  $( - 3,0 ]$ 
A)  $( - \infty , - 3 ] \cup [ 0 , \infty )$ 
B)  $( 0 , \infty )$ 
C)  $( - \infty , - 3 ) \cup ( 0 , \infty )$ 
D)  $( - 3,0 ]$

Question 2

Solve the equation.
-$$4 x ^ { 2 } + 5 x + 1 = 0$$

Accepted Answer

A)  $\left\{ \frac { 1 } { 4 } , - 1 \right\}$ 
B)  $\left\{ - \frac { 1 } { 4 } , - 1 \right\}$ 
C)  $\left\{ - \frac { 1 } { 4 } , 1 \right\}$ 
D)  $\left\{ \frac { 1 } { 4 } , 1 \right\}$ 
A)  $\left\{ \frac { 1 } { 4 } , - 1 \right\}$ 
B)  $\left\{ - \frac { 1 } { 4 } , - 1 \right\}$ 
C)  $\left\{ - \frac { 1 } { 4 } , 1 \right\}$ 
D)  $\left\{ \frac { 1 } { 4 } , 1 \right\}$

Question 3

Use the quadratic formula to solve the equation.
-$$x ^ { 2 } + 14 x + 85 = 0$$

Accepted Answer

A)  $\{ - 7 - 36 i , - 7 + 36 i \}$ 
B)  $\{ - 7 - 6 i , - 7 + 6 i \}$ 
C)  $\{ - 7 + 6 i \}$ 
D)  $\{ - 13 , - 1 \}$ 
A)  $\{ - 7 - 36 i , - 7 + 36 i \}$ 
B)  $\{ - 7 - 6 i , - 7 + 6 i \}$ 
C)  $\{ - 7 + 6 i \}$ 
D)  $\{ - 13 , - 1 \}$

Question 4

Fill in the blank with one of the words or phrases listed below.

-$\mathrm { A } ( \mathrm { n } )$ــــــــــــــــ equation is one that can be written in the form $a x ^ { 2 } + b x + c = 0$, where $a , b$, and $c$ are real numbers and a is not 0 .

Accepted Answer

A)  quadratic inequality 
B)  quadratic formula 
C)  discriminant 
D)  quadratic 
A)  quadratic inequality 
B)  quadratic formula 
C)  discriminant 
D)  quadratic

Question 5

Solve.
-A common equation used in business is a demand equation. It expresses the relationship between the unit price of some commodity and the quantity demanded. In the demand equation $p = - x ^ { 2 } + 107$, for a certain style of calculator, $\mathrm { p }$ is the price per calculator in dollars and $\mathrm { x }$ is the quantity demanded in thousands. Find the demand for the calculator if the price is $\$ 7$ per calculator.

Accepted Answer

A)  11 thousand units 
B)  58 thousand units 
C)  50 thousand units 
D)  10 thousand units 
A)  11 thousand units 
B)  58 thousand units 
C)  50 thousand units 
D)  10 thousand units

Question 6

Find the vertex of the graph of the quadratic function.
-$$f ( x ) = - x ^ { 2 } - 14 x - 6$$

Accepted Answer

A)  $( - 7,43 )$ 
B)  $( 7 , - 153 )$ 
C)  $( 7 , - 55 )$ 
D)  $( - 14 , - 6 )$ 
A)  $( - 7,43 )$ 
B)  $( 7 , - 153 )$ 
C)  $( 7 , - 55 )$ 
D)  $( - 14 , - 6 )$

Question 7

Match the function with its graph.
-$f ( x ) = - x ^ { 2 } - 8 x - 7$

Accepted Answer

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

Question 8

Find the vertex of the graph of the quadratic function.
-$$f ( x ) = x ^ { 2 } + x - 1$$

Accepted Answer

A)  $( - 1 , - 1 )$ 
B)  $( 1,1 )$ 
C)  $\left( - \frac { 1 } { 2 } , - \frac { 5 } { 4 } \right)$ 
D)  $\left( \frac { 1 } { 2 } , - \frac { 1 } { 4 } \right)$ 
A)  $( - 1 , - 1 )$ 
B)  $( 1,1 )$ 
C)  $\left( - \frac { 1 } { 2 } , - \frac { 5 } { 4 } \right)$ 
D)  $\left( \frac { 1 } { 2 } , - \frac { 1 } { 4 } \right)$

Question 9

Solve the inequality. Write the solution set in interval notation.
-$$( x + 2 ) ( x - 1 ) \leq 0$$

Accepted Answer

A)  $( - \infty , - 2 ) \cup ( 1 , \infty )$ 
B)  $( - 2,1 )$ 
C)  $[ - 2,1 ]$ 
D)  $( - \infty , - 2 ] \cup [ 1 , \infty )$ 
A)  $( - \infty , - 2 ) \cup ( 1 , \infty )$ 
B)  $( - 2,1 )$ 
C)  $[ - 2,1 ]$ 
D)  $( - \infty , - 2 ] \cup [ 1 , \infty )$

Question 10

Solve.
-An express train travels 334 miles between two cities. During the first 126 miles of a trip, the train traveled through mountainous terrain. The train traveled 10 miles per hour slower through mountainous terrain than
Through level terrain. If the total time to travel between the cities was 7 hours, find the speed of the train on
Level terrain.

Accepted Answer

A)  42 mph 
B)  62 mph 
C)  52 mph 
D)  32 mph 
A)  42 mph 
B)  62 mph 
C)  52 mph 
D)  32 mph

Question 11

Use the discriminant to determine the number and type of solutions of the equation.
-$$x ^ { 2 } + 6 x - 7 = 0$$

Accepted Answer

A)  Two real solutions 
B)  Two complex but not real solutions 
C)  One real solution 
A)  Two real solutions 
B)  Two complex but not real solutions 
C)  One real solution

Solve the inequality. Write the solution set in interval notation. - $\frac { x } { x + 3 } > 0$

Solve the equation. - $4 x ^ { 2 } + 5 x + 1 = 0$

Use the quadratic formula to solve the equation. - $x ^ { 2 } + 14 x + 85 = 0$

Find the vertex of the graph of the quadratic function. - $f ( x ) = - x ^ { 2 } - 14 x - 6$

Match the function with its graph. - $f ( x ) = - x ^ { 2 } - 8 x - 7$

Find the vertex of the graph of the quadratic function. - $f ( x ) = x ^ { 2 } + x - 1$

Solve the inequality. Write the solution set in interval notation. - $( x + 2 ) ( x - 1 ) \leq 0$

Use the discriminant to determine the number and type of solutions of the equation. - $x ^ { 2 } + 6 x - 7 = 0$

Real Numbers and Algebraic Expressions

Equations, Inequalities, and Problem Solving

Graphs and Functions

Systems of Equations and Inequalities

Polynomials and Polynomial Functions

Rational Expressions

Rational Exponents, Radicals, and Complex Numbers

Exponential and Logarithmic Functions

Conic Sections

Fractions

Filters

Exam 8: Quadratic Equations and Functions

Solve the inequality. Write the solution set in interval notation. - xx+3>0\frac { x } { x + 3 } > 0x+3x​>0

Solve the equation. - 4x2+5x+1=04 x ^ { 2 } + 5 x + 1 = 04x2+5x+1=0

Use the quadratic formula to solve the equation. - x2+14x+85=0x ^ { 2 } + 14 x + 85 = 0x2+14x+85=0

Fill in the blank with one of the words or phrases listed below. - A(n)\mathrm { A } ( \mathrm { n } )A(n) ــــــــــــــــ equation is one that can be written in the form ax2+bx+c=0a x ^ { 2 } + b x + c = 0ax2+bx+c=0 , where a,ba , ba,b , and ccc are real numbers and a is not 0 .

Find the vertex of the graph of the quadratic function. - f(x)=−x2−14x−6f ( x ) = - x ^ { 2 } - 14 x - 6f(x)=−x2−14x−6

Match the function with its graph. - f(x)=−x2−8x−7f ( x ) = - x ^ { 2 } - 8 x - 7f(x)=−x2−8x−7

Find the vertex of the graph of the quadratic function. - f(x)=x2+x−1f ( x ) = x ^ { 2 } + x - 1f(x)=x2+x−1

Solve the inequality. Write the solution set in interval notation. - (x+2)(x−1)≤0( x + 2 ) ( x - 1 ) \leq 0(x+2)(x−1)≤0

Use the discriminant to determine the number and type of solutions of the equation. - x2+6x−7=0x ^ { 2 } + 6 x - 7 = 0x2+6x−7=0