Question 1

Find the zeros of the function. Give exact answers.
-$$f ( x ) = x ^ { 2 } - 2 x - 3$$

Accepted Answer

A)  1,3 
B)  $- 1 , - 3$ 
C)  $1 , - 3$ 
D)  $- 1,3$ 
A)  1,3 
B)  $- 1 , - 3$ 
C)  $1 , - 3$ 
D)  $- 1,3$ D

Question 2

Match the equation to the correct graph.
-$$y = ( x - 3 ) ^ { 2 }$$

Accepted Answer

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

Question 3

Find the range of the given function.
-$$f ( x ) = 3 x ^ { 2 } + 24 x + 51$$

Accepted Answer

A)  $[ 3 , \infty )$ 
B)  $( - \infty , 4 ]$ 
C)  $( - \infty , - 3 ]$ 
D)  $[ - 4 , \infty )$ 
A)  $[ 3 , \infty )$ 
B)  $( - \infty , 4 ]$ 
C)  $( - \infty , - 3 ]$ 
D)  $[ - 4 , \infty )$ A

Question 4

Consider only the discriminant, $b ^ { 2 } - 4 a c$ to determine whether one real-number solution, two different real-number
solutions, or two different imaginary-number solutions exist.
-$$x ^ { 2 } + 4 x + 5 = 0$$

Accepted Answer

A)  Two different real-number solutions 
B)  One real solution 
C)  Two different imaginary-number solutions 
A)  Two different real-number solutions 
B)  One real solution 
C)  Two different imaginary-number solutions

Question 5

Solve.
-$$5 x ^ { 2 } + 5 = 25$$

Accepted Answer

A)  $12.5$ 
B)  2 
C)  $\pm 2$ 
D)  $\pm 3$ 
A)  $12.5$ 
B)  2 
C)  $\pm 2$ 
D)  $\pm 3$

Question 6

Solve.
-$3 x ^ { 2 } = 45$

Accepted Answer

A)  $22.5$ 
B)  $\pm 15$ 
C)  $\pm \sqrt { 15 }$ 
D)  16 
A)  $22.5$ 
B)  $\pm 15$ 
C)  $\pm \sqrt { 15 }$ 
D)  16

Question 7

Solve.
-$$x ^ { 1 / 3 } = - 5$$

Accepted Answer

A)  $- 15$ 
B)  $- 125$ 
C)  $- 243$ 
D)  No solution 
A)  $- 15$ 
B)  $- 125$ 
C)  $- 243$ 
D)  No solution

Question 8

Graph.
-$$f ( x ) = \frac { 1 } { 3 } x ^ { 2 } - 3 x + 4$$

Accepted Answer

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

Question 9

Simplify.
-$( 3 i ) ^ { 5 }$

Accepted Answer

A)  $- 243$ 
B)  $243 \mathrm { i }$ 
C)  243 
D)  $- 243 \mathrm { i }$ 
A)  $- 243$ 
B)  $243 \mathrm { i }$ 
C)  243 
D)  $- 243 \mathrm { i }$

Question 10

Solve. $\sqrt { 2 x + 3 } - \sqrt { x + 1 } = 1$

Accepted Answer

A)  $- 3 , - 1$ 
B)  $3 , - 1$ 
C)  3 
D)  No solution
-Solve. $\sqrt { 2 x + 3 } - \sqrt { x + 1 } = 1$ 
A)  $- 3 , - 1$ 
B)  $3 , - 1$ 
C)  3 
D)  No solution 
A)  $- 3 , - 1$ 
B)  $3 , - 1$ 
C)  3 
D)  No solution
-Solve. $\sqrt { 2 x + 3 } - \sqrt { x + 1 } = 1$ 
A)  $- 3 , - 1$ 
B)  $3 , - 1$ 
C)  3 
D)  No solution

Question 11

State whether the function is linear or quadratic.
-$$f ( x ) = - 3 x ^ { 2 }$$

Accepted Answer

A)  Linear 
B)  Quadratic 
A)  Linear 
B)  Quadratic

Question 12

Find the vertex of the parabola.
-$$h ( x ) = \frac { 1 } { 2 } x ^ { 2 } - 4 x - \frac { 7 } { 2 }$$

Accepted Answer

A)  $\left( - 4 , \frac { 41 } { 2 } \right)$ 
B)  $\left( 2 , - \frac { 19 } { 2 } \right)$ 
C)  $\left( 4 , - \frac { 23 } { 2 } \right)$ 
D)  $\left( 4 , \frac { 13 } { 2 } \right)$ 
A)  $\left( - 4 , \frac { 41 } { 2 } \right)$ 
B)  $\left( 2 , - \frac { 19 } { 2 } \right)$ 
C)  $\left( 4 , - \frac { 23 } { 2 } \right)$ 
D)  $\left( 4 , \frac { 13 } { 2 } \right)$

Question 13

Find the axis of symmetry of the given function.
-$$f ( x ) = 3 x ^ { 2 } + 24 x + 53$$

Accepted Answer

A)  $x = - 4$ 
B)  $x = - 5$ 
C)  $x = 4$ 
D)  $x = 5$ 
A)  $x = - 4$ 
B)  $x = - 5$ 
C)  $x = 4$ 
D)  $x = 5$

Question 14

Simplify.
-¡16

Accepted Answer

A)  $\mathrm { i }$ 
B)  $- 1$ 
C)  $- \mathrm { i }$ 
D)  1 
A)  $\mathrm { i }$ 
B)  $- 1$ 
C)  $- \mathrm { i }$ 
D)  1

Question 15

Simplify. Write your answers in the form of a+bi, where a and b are real numbers.
-$\frac { 5 + i } { - 1 - 7 i }$

Accepted Answer

A)  $- \frac { 6 } { 25 } + \frac { 17 } { 25 } i$ 
B)  $- \frac { 6 } { 25 }$ 
C)  $- \frac { 6 } { 25 } - \frac { 17 } { 25 } \mathrm { i }$ 
D)  $\frac { 17 } { 25 } \mathrm { i }$ 
A)  $- \frac { 6 } { 25 } + \frac { 17 } { 25 } i$ 
B)  $- \frac { 6 } { 25 }$ 
C)  $- \frac { 6 } { 25 } - \frac { 17 } { 25 } \mathrm { i }$ 
D)  $\frac { 17 } { 25 } \mathrm { i }$

Question 16

Simplify. Write your answers in the form of a+bi, where a and b are real numbers.
-$$\frac { 1 - 5 i } { ( 1 + 5 i ) ^ { 2 } }$$

Accepted Answer

A)  $- \frac { 37 } { 338 } + \frac { 35 } { 169 }$ i 
B)  $- \frac { 37 } { 338 } + \frac { 55 } { 338 } \mathrm { i }$ 
C)  $\frac { 1 } { 676 } + \frac { 15 } { 676 }$ i 
D)  $- \frac { 37 } { 338 } - \frac { 55 } { 338 } \mathrm { i }$ 
A)  $- \frac { 37 } { 338 } + \frac { 35 } { 169 }$ i 
B)  $- \frac { 37 } { 338 } + \frac { 55 } { 338 } \mathrm { i }$ 
C)  $\frac { 1 } { 676 } + \frac { 15 } { 676 }$ i 
D)  $- \frac { 37 } { 338 } - \frac { 55 } { 338 } \mathrm { i }$

Question 17

Simplify. Write your answers in the form of a+bi, where a and b are real numbers.
-$$\frac { 1 + 2 i } { ( 1 - 2 i ) ^ { 2 } }$$

Accepted Answer

A)  $- \frac { 11 } { 25 } - \frac { 1 } { 5 } \mathrm { i }$ 
B)  $\frac { 1 } { 25 } + \frac { 6 } { 25 }$ i 
C)  $- \frac { 11 } { 25 } + \frac { 14 } { 25 } \mathrm { i }$ 
D)  $- \frac { 11 } { 25 } - \frac { 2 } { 25 } \mathrm { i }$ 
A)  $- \frac { 11 } { 25 } - \frac { 1 } { 5 } \mathrm { i }$ 
B)  $\frac { 1 } { 25 } + \frac { 6 } { 25 }$ i 
C)  $- \frac { 11 } { 25 } + \frac { 14 } { 25 } \mathrm { i }$ 
D)  $- \frac { 11 } { 25 } - \frac { 2 } { 25 } \mathrm { i }$

Question 18

Solve.
-John owns a hotdog stand. He has found that his profit is represented by the function $\mathrm { P } ( \mathrm { x } ) = - \mathrm { x } ^ { 2 } + 74 \mathrm { x } + 80$, with $\mathrm { P } ( \mathrm { x } )$ being profits and $x$ the number of hotdogs sold. How many hotdogs must he sell to earn the most profit?

Accepted Answer

A)  21 hotdogs 
B)  43 hotdogs 
C)  38 hotdogs 
D)  37 hotdogs 
A)  21 hotdogs 
B)  43 hotdogs 
C)  38 hotdogs 
D)  37 hotdogs

Question 19

Find the axis of symmetry of the given function.
-$$g ( x ) = 7 x ^ { 2 } - 98 x + 353$$

Accepted Answer

A)  $x = 7$ 
B)  $x = - 10$ 
C)  $x = 10$ 
D)  $x = 0$ 
A)  $x = 7$ 
B)  $x = - 10$ 
C)  $x = 10$ 
D)  $x = 0$

Question 20

Match the equation to the correct graph.
-$$y = - ( x + 6 ) ^ { 2 } + 3$$

Accepted Answer

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

Find the zeros of the function. Give exact answers. - $f ( x ) = x ^ { 2 } - 2 x - 3$

Match the equation to the correct graph. - $y = ( x - 3 ) ^ { 2 }$

Find the range of the given function. - $f ( x ) = 3 x ^ { 2 } + 24 x + 51$

Consider only the discriminant, $b ^ { 2 } - 4 a c$ to determine whether one real-number solution, two different real-number solutions, or two different imaginary-number solutions exist. - $x ^ { 2 } + 4 x + 5 = 0$

Solve. - $5 x ^ { 2 } + 5 = 25$

Solve. - $3 x ^ { 2 } = 45$

Solve. - $x ^ { 1 / 3 } = - 5$

Graph. - $f ( x ) = \frac { 1 } { 3 } x ^ { 2 } - 3 x + 4$ $Graph. - f ( x ) = \frac { 1 } { 3 } x ^ { 2 } - 3 x + 4$

Simplify. - $( 3 i ) ^ { 5 }$

Solve. $\sqrt { 2 x + 3 } - \sqrt { x + 1 } = 1$ A) $- 3 , - 1$ B) $3 , - 1$ C) 3 D) No solution -Solve. $\sqrt { 2 x + 3 } - \sqrt { x + 1 } = 1$

State whether the function is linear or quadratic. - $f ( x ) = - 3 x ^ { 2 }$

Find the vertex of the parabola. - $h ( x ) = \frac { 1 } { 2 } x ^ { 2 } - 4 x - \frac { 7 } { 2 }$

Find the axis of symmetry of the given function. - $f ( x ) = 3 x ^ { 2 } + 24 x + 53$

Simplify. -¡16

Simplify. Write your answers in the form of a+bi, where a and b are real numbers. - $\frac { 5 + i } { - 1 - 7 i }$

Simplify. Write your answers in the form of a+bi, where a and b are real numbers. - $\frac { 1 - 5 i } { ( 1 + 5 i ) ^ { 2 } }$

Simplify. Write your answers in the form of a+bi, where a and b are real numbers. - $\frac { 1 + 2 i } { ( 1 - 2 i ) ^ { 2 } }$

Find the axis of symmetry of the given function. - $g ( x ) = 7 x ^ { 2 } - 98 x + 353$

Match the equation to the correct graph. - $y = - ( x + 6 ) ^ { 2 } + 3$

Graphs, Functions, and Models

More on Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Systems of Equations and Matrices

Conic Sections

Sequences, Series, and Combinatorics

Filters

Exam 3: Quadratic Functions and Equations; Inequalities

Find the zeros of the function. Give exact answers. - f(x)=x2−2x−3f ( x ) = x ^ { 2 } - 2 x - 3f(x)=x2−2x−3

Match the equation to the correct graph. - y=(x−3)2y = ( x - 3 ) ^ { 2 }y=(x−3)2

Find the range of the given function. - f(x)=3x2+24x+51f ( x ) = 3 x ^ { 2 } + 24 x + 51f(x)=3x2+24x+51

Consider only the discriminant, b2−4acb ^ { 2 } - 4 a cb2−4ac to determine whether one real-number solution, two different real-number solutions, or two different imaginary-number solutions exist. - x2+4x+5=0x ^ { 2 } + 4 x + 5 = 0x2+4x+5=0

Solve. - 5x2+5=255 x ^ { 2 } + 5 = 255x2+5=25

Solve. - 3x2=453 x ^ { 2 } = 453x2=45

Solve. - x1/3=−5x ^ { 1 / 3 } = - 5x1/3=−5

Graph. - f(x)=13x2−3x+4f ( x ) = \frac { 1 } { 3 } x ^ { 2 } - 3 x + 4f(x)=31​x2−3x+4

Simplify. - (3i)5( 3 i ) ^ { 5 }(3i)5

Solve. 2x+3−x+1=1\sqrt { 2 x + 3 } - \sqrt { x + 1 } = 12x+3​−x+1​=1 A) −3,−1- 3 , - 1−3,−1 B) 3,−13 , - 13,−1 C) 3 D) No solution -Solve. 2x+3−x+1=1\sqrt { 2 x + 3 } - \sqrt { x + 1 } = 12x+3​−x+1​=1

State whether the function is linear or quadratic. - f(x)=−3x2f ( x ) = - 3 x ^ { 2 }f(x)=−3x2

Find the vertex of the parabola. - h(x)=12x2−4x−72h ( x ) = \frac { 1 } { 2 } x ^ { 2 } - 4 x - \frac { 7 } { 2 }h(x)=21​x2−4x−27​

Find the axis of symmetry of the given function. - f(x)=3x2+24x+53f ( x ) = 3 x ^ { 2 } + 24 x + 53f(x)=3x2+24x+53