Question 1

Solve and write interval notation for the solution set.
-$| x | \leq 4.3$

Accepted Answer

A)  $( - \infty , - 4.3 ) \cup ( 4.3 , \infty )$ 
B)  $( - \infty , - 4 ) \cup ( 4 , \infty )$ 
C)  $[ - 4.3,4.3 ]$ 
D)  $( - \infty , - 4.3 ] \cup [ 4.3 , \infty )$ 
A)  $( - \infty , - 4.3 ) \cup ( 4.3 , \infty )$ 
B)  $( - \infty , - 4 ) \cup ( 4 , \infty )$ 
C)  $[ - 4.3,4.3 ]$ 
D)  $( - \infty , - 4.3 ] \cup [ 4.3 , \infty )$

Question 2

Solve.
-$$56 x + 8 x ^ { 2 } = 0$$

Accepted Answer

A)  $- 7$ 
B)  $0 , - 7$ 
C)  $- 8 , - 7$ 
D)  $- 28$ 
A)  $- 7$ 
B)  $0 , - 7$ 
C)  $- 8 , - 7$ 
D)  $- 28$

Question 3

Find the intervals on which the function is increasing and the intervals on which the function is decreasing.
-$$f ( x ) = x ^ { 2 } - 5 x + 6$$

Accepted Answer

A)  Increasing on $\left( \frac { 5 } { 2 } , \infty \right)$; decreasing on $\left( - \infty , \frac { 5 } { 2 } \right)$ 
B)  Increasing on $\left( - \frac { 5 } { 2 } , \infty \right) ;$ decreasing on $\left( - \infty , - \frac { 5 } { 2 } \right)$ 
C)  Increasing on $\left( - \infty , - \frac { 5 } { 2 } \right) ;$ decreasing on $\left( - \frac { 5 } { 2 } , \infty \right)$ 
D)  Increasing on $\left( - \infty , \frac { 5 } { 2 } \right)$; decreasing on $\left( \frac { 5 } { 2 } , \infty \right)$ 
A)  Increasing on $\left( \frac { 5 } { 2 } , \infty \right)$; decreasing on $\left( - \infty , \frac { 5 } { 2 } \right)$ 
B)  Increasing on $\left( - \frac { 5 } { 2 } , \infty \right) ;$ decreasing on $\left( - \infty , - \frac { 5 } { 2 } \right)$ 
C)  Increasing on $\left( - \infty , - \frac { 5 } { 2 } \right) ;$ decreasing on $\left( - \frac { 5 } { 2 } , \infty \right)$ 
D)  Increasing on $\left( - \infty , \frac { 5 } { 2 } \right)$; decreasing on $\left( \frac { 5 } { 2 } , \infty \right)$

Question 4

Match the equation to the correct graph.
-$$y = 2 ( x + 2 ) ^ { 2 } - 4$$

Accepted Answer

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

Question 5

Use the quadratic formula to find the exact solutions.
-$$3 x ^ { 2 } - 20 x - 7 = 0$$

Accepted Answer

A)  $- \frac { 1 } { 3 } , 7$ 
B)  $- \frac { 1 } { 7 } , 3$ 
C)  $- 3,7$ 
D)  $- \frac { 1 } { 7 } , - 3$ 
A)  $- \frac { 1 } { 3 } , 7$ 
B)  $- \frac { 1 } { 7 } , 3$ 
C)  $- 3,7$ 
D)  $- \frac { 1 } { 7 } , - 3$

Question 6

Solve the inequality and graph the solution set.
-$$| 4 x - 7 | \geq 8$$

Accepted Answer

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

Question 7

Solve and write interval notation for the solution set.
-$| x | > 5$

Accepted Answer

A)  $( - \infty , - 5 ) \cup ( 5 , \infty )$ 
B)  $( - 5 , \infty )$ 
C)  $( 5 , \infty )$ 
D)  $( - 5,5 )$ 
A)  $( - \infty , - 5 ) \cup ( 5 , \infty )$ 
B)  $( - 5 , \infty )$ 
C)  $( 5 , \infty )$ 
D)  $( - 5,5 )$

Question 8

Simplify. Write your answers in the form of a+bi, where a and b are real numbers.
-$$\sqrt { - 25 } \cdot \sqrt { - 64 }$$

Accepted Answer

A)  $- 40$ 
B)  40 
C)  $40 \mathrm { i } ^ { 2 }$ 
D)  $- 40 \mathrm { i }$ 
A)  $- 40$ 
B)  40 
C)  $40 \mathrm { i } ^ { 2 }$ 
D)  $- 40 \mathrm { i }$

Question 9

Solve the inequality and graph the solution set.
-$$| 8 x - 9 | > - 8$$

Accepted Answer

A) 
  
B) 
  
C)  $( - \infty , \infty )$
  
D) 
  
A) 
  
B) 
  
C)  $( - \infty , \infty )$
  
D)

Question 10

State whether the function is linear or quadratic.
-$$f ( x ) = 0.6 x ^ { 2 } + 10 x + 21$$

Accepted Answer

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

Question 11

Find the vertex of the parabola.
-$$f ( x ) = - \frac { 1 } { 3 } x ^ { 2 } + 9 x - 3$$

Accepted Answer

A)  $( 27 , - 3 )$ 
B)  $\left( \frac { 27 } { 2 } , \frac { 231 } { 4 } \right)$ 
C)  $( - 27 , - 489 )$ 
D)  $\left( - \frac { 27 } { 2 } , - \frac { 741 } { 4 } \right)$ 
A)  $( 27 , - 3 )$ 
B)  $\left( \frac { 27 } { 2 } , \frac { 231 } { 4 } \right)$ 
C)  $( - 27 , - 489 )$ 
D)  $\left( - \frac { 27 } { 2 } , - \frac { 741 } { 4 } \right)$

Question 12

Use a graphing calculator to find the zeros of the function. Round to three decimal places.
-$$f ( x ) = 1.18 x ^ { 2 } - 13.37 x - 1.94$$

Accepted Answer

A)  $- 0.287,22.948$ 
B)  $0.147,11.184$ 
C)  $- 11.474,0.143$ 
D)  $- 0.143,11.474$ 
A)  $- 0.287,22.948$ 
B)  $0.147,11.184$ 
C)  $- 11.474,0.143$ 
D)  $- 0.143,11.474$

Question 13

State whether the function is linear or quadratic.
-$$f ( x ) = 4 x + ( 1.9 ) ^ { 2 }$$

Accepted Answer

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

Question 14

Solve the problem.
-The area of a square is 81 square centimeters. If the same amount is added to one dimension and removed from the other, the resulting rectangle has an area 9 square centimeters less than the area
Of the square. How much is added and subtracted?

Accepted Answer

A) 12 cm 
B) 3 cm 
C) 4 cm 
D) 9 cm 
A) 12 cm 
B) 3 cm 
C) 4 cm 
D) 9 cm

Question 15

Solve.
-$$5 x ^ { 2 } + 35 = 0$$

Accepted Answer

A)  $17.5$ 
B)  $\pm 7 \mathrm { i }$ 
C)  $\pm \sqrt { 7 } \mathrm { i }$ 
D)  8 
A)  $17.5$ 
B)  $\pm 7 \mathrm { i }$ 
C)  $\pm \sqrt { 7 } \mathrm { i }$ 
D)  8

Question 16

Solve.
-$\sqrt { 3 x - 2 } + \sqrt { 11 + x } = - 1$

Accepted Answer

A)  0 
B)  $- \frac { 5 } { 2 }$ 
C)  5 
D)  No solution 
A)  0 
B)  $- \frac { 5 } { 2 }$ 
C)  5 
D)  No solution

Question 17

Solve.
-John owns a hotdog stand. His profit is represented by $P ( x ) = - x ^ { 2 } + 14 x + 55$, with $P ( x )$ being profit and $x$ the number of hotdogs sold. What is the most he can earn?

Accepted Answer

A)  $\$ 49$ 
B)  $\$ 104$ 
C)  $\$ 111$ 
D)  $\$ 90$ 
A)  $\$ 49$ 
B)  $\$ 104$ 
C)  $\$ 111$ 
D)  $\$ 90$

Question 18

Find the zeros of the function. Give exact answers.
-$$f ( x ) = x ^ { 2 } - 9 x - 9$$

Accepted Answer

A)  $\frac { - 9 \pm 3 \sqrt { 5 } } { 2 }$ 
B)  $\frac { 9 \pm 3 \sqrt { 13 } } { 2 }$ 
C)  $\frac { - 9 \pm 3 \sqrt { 13 } } { 2 }$ 
D)  $\frac { 9 \pm 3 \sqrt { 5 } } { 2 }$ 
A)  $\frac { - 9 \pm 3 \sqrt { 5 } } { 2 }$ 
B)  $\frac { 9 \pm 3 \sqrt { 13 } } { 2 }$ 
C)  $\frac { - 9 \pm 3 \sqrt { 13 } } { 2 }$ 
D)  $\frac { 9 \pm 3 \sqrt { 5 } } { 2 }$

Question 19

Simplify. Write your answers in the form of a+bi, where a and b are real numbers.
-$$( 7 - 3 \mathrm { i } ) ^ { 2 }$$

Accepted Answer

A)  $58 - 42 \mathrm { i }$ 
B)  $40 - 42 \mathrm { i }$ 
C)  $40 + 42 i$ 
D)  $58 + 42 \mathrm { i }$ 
A)  $58 - 42 \mathrm { i }$ 
B)  $40 - 42 \mathrm { i }$ 
C)  $40 + 42 i$ 
D)  $58 + 42 \mathrm { i }$

Question 20

Find the zeros of the function. Give exact answers.
-$$f ( x ) = 3 x ^ { 2 } - x + 6$$

Accepted Answer

A)  $\frac { 1 } { 3 } \pm \frac { \sqrt { 71 } } { 3 }$ i 
B)  $1 \pm \sqrt { 71 }$ 
C)  $\frac { 1 } { 6 } \pm \frac { \sqrt { 71 } } { 6 } \mathrm { i }$ 
D)  $- \frac { 1 } { 3 } , \frac { 1 } { 6 }$ 
A)  $\frac { 1 } { 3 } \pm \frac { \sqrt { 71 } } { 3 }$ i 
B)  $1 \pm \sqrt { 71 }$ 
C)  $\frac { 1 } { 6 } \pm \frac { \sqrt { 71 } } { 6 } \mathrm { i }$ 
D)  $- \frac { 1 } { 3 } , \frac { 1 } { 6 }$

Solve and write interval notation for the solution set. - $| x | \leq 4.3$

Solve. - $56 x + 8 x ^ { 2 } = 0$

Find the intervals on which the function is increasing and the intervals on which the function is decreasing. - $f ( x ) = x ^ { 2 } - 5 x + 6$

Match the equation to the correct graph. - $y = 2 ( x + 2 ) ^ { 2 } - 4$

Use the quadratic formula to find the exact solutions. - $3 x ^ { 2 } - 20 x - 7 = 0$

Solve the inequality and graph the solution set. - $| 4 x - 7 | \geq 8$ $Solve the inequality and graph the solution set. - | 4 x - 7 | \geq 8$

Solve and write interval notation for the solution set. - $| x | > 5$

Simplify. Write your answers in the form of a+bi, where a and b are real numbers. - $\sqrt { - 25 } \cdot \sqrt { - 64 }$

Solve the inequality and graph the solution set. - $| 8 x - 9 | > - 8$

State whether the function is linear or quadratic. - $f ( x ) = 0.6 x ^ { 2 } + 10 x + 21$

Find the vertex of the parabola. - $f ( x ) = - \frac { 1 } { 3 } x ^ { 2 } + 9 x - 3$

Use a graphing calculator to find the zeros of the function. Round to three decimal places. - $f ( x ) = 1.18 x ^ { 2 } - 13.37 x - 1.94$

State whether the function is linear or quadratic. - $f ( x ) = 4 x + ( 1.9 ) ^ { 2 }$

Solve the problem. -The area of a square is 81 square centimeters. If the same amount is added to one dimension and removed from the other, the resulting rectangle has an area 9 square centimeters less than the area Of the square. How much is added and subtracted?

Solve. - $5 x ^ { 2 } + 35 = 0$

Solve. - $\sqrt { 3 x - 2 } + \sqrt { 11 + x } = - 1$

Solve. -John owns a hotdog stand. His profit is represented by $P ( x ) = - x ^ { 2 } + 14 x + 55$ , with $P ( x )$ being profit and $x$ the number of hotdogs sold. What is the most he can earn?

Find the zeros of the function. Give exact answers. - $f ( x ) = x ^ { 2 } - 9 x - 9$

Simplify. Write your answers in the form of a+bi, where a and b are real numbers. - $( 7 - 3 \mathrm { i } ) ^ { 2 }$

Find the zeros of the function. Give exact answers. - $f ( x ) = 3 x ^ { 2 } - x + 6$

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Exam 3: Quadratic Functions and Equations; Inequalities

Solve and write interval notation for the solution set. - ∣x∣≤4.3| x | \leq 4.3∣x∣≤4.3

Solve. - 56x+8x2=056 x + 8 x ^ { 2 } = 056x+8x2=0

Find the intervals on which the function is increasing and the intervals on which the function is decreasing. - f(x)=x2−5x+6f ( x ) = x ^ { 2 } - 5 x + 6f(x)=x2−5x+6

Match the equation to the correct graph. - y=2(x+2)2−4y = 2 ( x + 2 ) ^ { 2 } - 4y=2(x+2)2−4

Use the quadratic formula to find the exact solutions. - 3x2−20x−7=03 x ^ { 2 } - 20 x - 7 = 03x2−20x−7=0

Solve the inequality and graph the solution set. - ∣4x−7∣≥8| 4 x - 7 | \geq 8∣4x−7∣≥8

Solve and write interval notation for the solution set. - ∣x∣>5| x | > 5∣x∣>5

Simplify. Write your answers in the form of a+bi, where a and b are real numbers. - −25⋅−64\sqrt { - 25 } \cdot \sqrt { - 64 }−25​⋅−64​

Solve the inequality and graph the solution set. - ∣8x−9∣>−8| 8 x - 9 | > - 8∣8x−9∣>−8

State whether the function is linear or quadratic. - f(x)=0.6x2+10x+21f ( x ) = 0.6 x ^ { 2 } + 10 x + 21f(x)=0.6x2+10x+21

Find the vertex of the parabola. - f(x)=−13x2+9x−3f ( x ) = - \frac { 1 } { 3 } x ^ { 2 } + 9 x - 3f(x)=−31​x2+9x−3

Use a graphing calculator to find the zeros of the function. Round to three decimal places. - f(x)=1.18x2−13.37x−1.94f ( x ) = 1.18 x ^ { 2 } - 13.37 x - 1.94f(x)=1.18x2−13.37x−1.94

State whether the function is linear or quadratic. - f(x)=4x+(1.9)2f ( x ) = 4 x + ( 1.9 ) ^ { 2 }f(x)=4x+(1.9)2