Question 1

Find the vertex of the function. $$f ( x ) = - 3 ( x - 19 ) ^ { 2 } + 16$$

Accepted Answer

A)  (-19, 16) 
B)  (16, 19) 
C)  (19, 16) 
D)  (16, -19) 
A)  (-19, 16) 
B)  (16, 19) 
C)  (19, 16) 
D)  (16, -19)

Question 2

Find the value of n so that the expression is a perfect square trinomial and then factor the trinomial. $$x ^ { 2 } + 20 x + n$$

Accepted Answer

A)  $n = 100 ; ( x + 10 ) ( x - 10 )$ 
B)  $n = 100 ; ( x + 10 ) ^ { 2 }$ 
C)  $n = 400 ; ( x + 20 ) ^ { 2 }$ 
D)  $n = 100 ; ( x - 10 ) ^ { 2 }$ 
A)  $n = 100 ; ( x + 10 ) ( x - 10 )$ 
B)  $n = 100 ; ( x + 10 ) ^ { 2 }$ 
C)  $n = 400 ; ( x + 20 ) ^ { 2 }$ 
D)  $n = 100 ; ( x - 10 ) ^ { 2 }$

Question 3

A square has an area of 87 square inches. What are the lengths of the sides? (Round to one decimal place if necessary.)

Accepted Answer

A)  9.3 in. 
B)  348 in. 
C)  21.8 in. 
D)  7569 in. 
A)  9.3 in. 
B)  348 in. 
C)  21.8 in. 
D)  7569 in.

Question 4

Solve the equation by using substitution. $z ^ { 4 } - 256 = 0$

Accepted Answer

A)  $\{ 4 , - 4 \}$ 
B)  $\{ 4 , - 4,16 i , - 16 i \}$ 
C)  $\{ 4 \}$ 
D)  $\{ 4 , - 4,4 i , - 4 i \}$ 
A)  $\{ 4 , - 4 \}$ 
B)  $\{ 4 , - 4,16 i , - 16 i \}$ 
C)  $\{ 4 \}$ 
D)  $\{ 4 , - 4,4 i , - 4 i \}$

Question 5

a. Find the vertex.
b. Find the y-intercept.
c. Find the x-intercept(s), if they exist.
d. Use this information to graph the function. $$f ( x ) = - x ^ { 2 } - 3 x + 4$$

Accepted Answer

The answer of a. Find the vertex.
b. Find the y-intercept.
c....

Question 6

Solve the equation by using the quadratic formula. $6 y + 3 = - 4 y ^ { 2 }$

Accepted Answer

A)  $\left\{ - \frac { 1 } { 4 } + \frac { \sqrt { 105 } } { 12 } , - \frac { 1 } { 4 } - \frac { \sqrt { 105 } } { 12 } \right\}$ 
B)  $\left\{ - \frac { 9 } { 2 } , \frac { 1 } { 3 } \right\}$ 
C)  $\left\{ - \frac { 3 } { 4 } + \frac { i \sqrt { 3 } } { 4 } , - \frac { 3 } { 4 } - \frac { i \sqrt { 3 } } { 4 } \right\}$ 
D)  $\{ 2 + \sqrt { 3 } , 2 - \sqrt { 3 } \}$ 
A)  $\left\{ - \frac { 1 } { 4 } + \frac { \sqrt { 105 } } { 12 } , - \frac { 1 } { 4 } - \frac { \sqrt { 105 } } { 12 } \right\}$ 
B)  $\left\{ - \frac { 9 } { 2 } , \frac { 1 } { 3 } \right\}$ 
C)  $\left\{ - \frac { 3 } { 4 } + \frac { i \sqrt { 3 } } { 4 } , - \frac { 3 } { 4 } - \frac { i \sqrt { 3 } } { 4 } \right\}$ 
D)  $\{ 2 + \sqrt { 3 } , 2 - \sqrt { 3 } \}$

Question 7

Estimate from the graph the intervals for which the inequality is true. $f(x) \geq 0$

Accepted Answer

The answer of Estimate from the graph the intervals for...

Question 8

Graph the function. $$h ( x ) = - 4 x ^ { 2 }$$

Accepted Answer

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

Question 9

Estimate from the graph the intervals for which the inequality is true. $f ( x ) < 0$

Accepted Answer

The answer of Estimate from the graph the intervals for...

Question 10

Solve the equation by using the square root property. $$2 y ^ { 2 } = - 36$$

Accepted Answer

A)  $\{ 3 , - 3 \}$ 
B)  $\{ 3 i , - 3 i \}$ 
C)  $\{ 3 i \sqrt { 2 } , - 3 i \sqrt { 2 } \}$ 
D)  $\{ 3 \sqrt { 2 } \}$ 
A)  $\{ 3 , - 3 \}$ 
B)  $\{ 3 i , - 3 i \}$ 
C)  $\{ 3 i \sqrt { 2 } , - 3 i \sqrt { 2 } \}$ 
D)  $\{ 3 \sqrt { 2 } \}$

Question 11

Solve the equation by using the square root property. $$2 n ^ { 2 } + 18 = 42$$

Accepted Answer

The answer of Solve the equation by using the square...

Question 12

Solve the quadratic equation by completing the square and applying the square root property. $$- 3 y - 40 = - y ^ { 2 }$$

Accepted Answer

A)  {-8i, 5i} 
B)  {-8, 5} 
C)  {-5, 8} 
D)  {-5i, 8i} 
A)  {-8i, 5i} 
B)  {-8, 5} 
C)  {-5, 8} 
D)  {-5i, 8i}

Question 13

Solve the equation by using the square root property. $$2 x ^ { 2 } = 18$$

Accepted Answer

The answer of Solve the equation by using the square...

Question 14

Solve the equation by using the square root property. $$y ^ { 2 } = 25$$

Accepted Answer

The answer of Solve the equation by using the square...

Question 15

Solve the equation. $$x + \frac { 9 } { 4 x } = \frac { 37 } { 4 }$$

Accepted Answer

A)  $\left\{ \frac { \sqrt { 26 } } { 2 } \right\}$ 
B)  $\left\{ - \frac { 1 } { 4 } , - 9 \right\}$ 
C)  $\left\{ \frac { 1 } { 4 } , 9 \right\}$ 
D)  $\left\{ \pm \frac { \sqrt { 26 } } { 2 } \right\}$ 
A)  $\left\{ \frac { \sqrt { 26 } } { 2 } \right\}$ 
B)  $\left\{ - \frac { 1 } { 4 } , - 9 \right\}$ 
C)  $\left\{ \frac { 1 } { 4 } , 9 \right\}$ 
D)  $\left\{ \pm \frac { \sqrt { 26 } } { 2 } \right\}$

Question 16

Solve the polynomial inequality. Write the answer in interval notation. $$( 6 x - 18 ) ( x + 7 ) > 0$$

Accepted Answer

A)  $( - \infty , - 7 ) \cup ( 3 , \infty )$ 
B)  $( - \infty , - 3 ) \cup ( 7 , \infty )$ 
C)  $[ - 7,3 ]$ 
D)  $( - 7,3 )$ 
A)  $( - \infty , - 7 ) \cup ( 3 , \infty )$ 
B)  $( - \infty , - 3 ) \cup ( 7 , \infty )$ 
C)  $[ - 7,3 ]$ 
D)  $( - 7,3 )$

Question 17

Solve the equation by using the square root property. $$( 3 x + 6 ) ^ { 2 } = 49$$

Accepted Answer

The answer of Solve the equation by using the square...

Question 18

A catapult is designed to launch circus performers from a raised platform. After launch, the height of the performer in feet is given by $h ( t ) = - 16 t ^ { 2 } + 80 t + 32$ where t is seconds after launch. After how many seconds is the performer exactly 100 feet above the Ground? Round to the nearest tenth of a second.

Accepted Answer

A)  5 seconds 
B)  1.1 and 3.9 seconds 
C)  -0.4 and 5.4 seconds 
D)  0.5 and 2.8 seconds 
A)  5 seconds 
B)  1.1 and 3.9 seconds 
C)  -0.4 and 5.4 seconds 
D)  0.5 and 2.8 seconds

Question 19

Find the x- and y-intercepts of the function. $$f ( x ) = 4 x ^ { 2 } - 40$$

Accepted Answer

A)  x-intercepts: ( 10, 0) and (- 10, 0); y-intercept: (0, -40) 
B)  x-intercept: ( 10, 0); y-intercept: none 
C)  x-intercepts: (0, 10) and (0, - 10); y-intercept: (-40, 0) 
D)  x-intercept: (0, 10); y-intercept: (-40, 0) 
A)  x-intercepts: ( 10, 0) and (- 10, 0); y-intercept: (0, -40) 
B)  x-intercept: ( 10, 0); y-intercept: none 
C)  x-intercepts: (0, 10) and (0, - 10); y-intercept: (-40, 0) 
D)  x-intercept: (0, 10); y-intercept: (-40, 0)

Question 20

Graph the function. $$g ( x ) = \frac { 1 } { 4 } ( x - 2 ) ^ { 2 } - 4$$

Accepted Answer

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

Find the vertex of the function. $f ( x ) = - 3 ( x - 19 ) ^ { 2 } + 16$

Find the value of n so that the expression is a perfect square trinomial and then factor the trinomial. $x ^ { 2 } + 20 x + n$

A square has an area of 87 square inches. What are the lengths of the sides? (Round to one decimal place if necessary.)

Solve the equation by using substitution. $z ^ { 4 } - 256 = 0$

a. Find the vertex. b. Find the y-intercept. c. Find the x-intercept(s), if they exist. d. Use this information to graph the function. $f ( x ) = - x ^ { 2 } - 3 x + 4$

Solve the equation by using the quadratic formula. $6 y + 3 = - 4 y ^ { 2 }$

Estimate from the graph the intervals for which the inequality is true. $f(x) \geq 0$ $Estimate from the graph the intervals for which the inequality is true. f(x) \geq 0$

Graph the function. $h ( x ) = - 4 x ^ { 2 }$

Estimate from the graph the intervals for which the inequality is true. $f ( x ) < 0$

Solve the equation by using the square root property. $2 y ^ { 2 } = - 36$

Solve the equation by using the square root property. $2 n ^ { 2 } + 18 = 42$

Solve the quadratic equation by completing the square and applying the square root property. $- 3 y - 40 = - y ^ { 2 }$

Solve the equation by using the square root property. $2 x ^ { 2 } = 18$

Solve the equation by using the square root property. $y ^ { 2 } = 25$

Solve the equation. $x + \frac { 9 } { 4 x } = \frac { 37 } { 4 }$

Solve the polynomial inequality. Write the answer in interval notation. $( 6 x - 18 ) ( x + 7 ) > 0$

Solve the equation by using the square root property. $( 3 x + 6 ) ^ { 2 } = 49$

Find the x- and y-intercepts of the function. $f ( x ) = 4 x ^ { 2 } - 40$

Graph the function. $g ( x ) = \frac { 1 } { 4 } ( x - 2 ) ^ { 2 } - 4$

Linear Equations and Inequalities in One Variable

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Exam 7: Quadratic Equations, Functions and Inequalities

Find the vertex of the function. f(x)=−3(x−19)2+16f ( x ) = - 3 ( x - 19 ) ^ { 2 } + 16f(x)=−3(x−19)2+16

Find the value of n so that the expression is a perfect square trinomial and then factor the trinomial. x2+20x+nx ^ { 2 } + 20 x + nx2+20x+n

A square has an area of 87 square inches. What are the lengths of the sides? (Round to one decimal place if necessary.)

Solve the equation by using substitution. z4−256=0z ^ { 4 } - 256 = 0z4−256=0

a. Find the vertex. b. Find the y-intercept. c. Find the x-intercept(s), if they exist. d. Use this information to graph the function. f(x)=−x2−3x+4f ( x ) = - x ^ { 2 } - 3 x + 4f(x)=−x2−3x+4

Solve the equation by using the quadratic formula. 6y+3=−4y26 y + 3 = - 4 y ^ { 2 }6y+3=−4y2

Estimate from the graph the intervals for which the inequality is true. f(x)≥0f(x) \geq 0f(x)≥0

Graph the function. h(x)=−4x2h ( x ) = - 4 x ^ { 2 }h(x)=−4x2

Estimate from the graph the intervals for which the inequality is true. f(x)<0f ( x ) < 0f(x)<0

Solve the equation by using the square root property. 2y2=−362 y ^ { 2 } = - 362y2=−36

Solve the equation by using the square root property. 2n2+18=422 n ^ { 2 } + 18 = 422n2+18=42

Solve the quadratic equation by completing the square and applying the square root property. −3y−40=−y2- 3 y - 40 = - y ^ { 2 }−3y−40=−y2

Solve the equation by using the square root property. 2x2=182 x ^ { 2 } = 182x2=18

Solve the equation by using the square root property. y2=25y ^ { 2 } = 25y2=25

Solve the equation. x+94x=374x + \frac { 9 } { 4 x } = \frac { 37 } { 4 }x+4x9​=437​

Solve the polynomial inequality. Write the answer in interval notation. (6x−18)(x+7)>0( 6 x - 18 ) ( x + 7 ) > 0(6x−18)(x+7)>0

Solve the equation by using the square root property. (3x+6)2=49( 3 x + 6 ) ^ { 2 } = 49(3x+6)2=49

Find the x- and y-intercepts of the function. f(x)=4x2−40f ( x ) = 4 x ^ { 2 } - 40f(x)=4x2−40

Graph the function. g(x)=14(x−2)2−4g ( x ) = \frac { 1 } { 4 } ( x - 2 ) ^ { 2 } - 4g(x)=41​(x−2)2−4

Linear Equations and Inequalities in One Variable

Linear Equations in Two Variables and Functions

Systems of Linear Equations and Inequalities

Polynomials

Rational Expressions and Rational Equations

Radicals and Complex Numbers

Exponential and Logarithmic Functions and Applications

Conic Sections

Binomial Expansions, Sequences, and Series

Online: Transformations, Piecewise-Defined Functions, and Probability

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Find the vertex of the function. $f ( x ) = - 3 ( x - 19 ) ^ { 2 } + 16$

Find the value of n so that the expression is a perfect square trinomial and then factor the trinomial. $x ^ { 2 } + 20 x + n$

Solve the equation by using substitution. $z ^ { 4 } - 256 = 0$

a. Find the vertex. b. Find the y-intercept. c. Find the x-intercept(s), if they exist. d. Use this information to graph the function. $f ( x ) = - x ^ { 2 } - 3 x + 4$

Solve the equation by using the quadratic formula. $6 y + 3 = - 4 y ^ { 2 }$

Estimate from the graph the intervals for which the inequality is true. $f(x) \geq 0$ $Estimate from the graph the intervals for which the inequality is true. f(x) \geq 0$

Graph the function. $h ( x ) = - 4 x ^ { 2 }$

Estimate from the graph the intervals for which the inequality is true. $f ( x ) < 0$

Solve the equation by using the square root property. $2 y ^ { 2 } = - 36$

Solve the equation by using the square root property. $2 n ^ { 2 } + 18 = 42$

Solve the quadratic equation by completing the square and applying the square root property. $- 3 y - 40 = - y ^ { 2 }$

Solve the equation by using the square root property. $2 x ^ { 2 } = 18$

Solve the equation by using the square root property. $y ^ { 2 } = 25$

Solve the equation. $x + \frac { 9 } { 4 x } = \frac { 37 } { 4 }$

Solve the polynomial inequality. Write the answer in interval notation. $( 6 x - 18 ) ( x + 7 ) > 0$

Solve the equation by using the square root property. $( 3 x + 6 ) ^ { 2 } = 49$

Find the x- and y-intercepts of the function. $f ( x ) = 4 x ^ { 2 } - 40$

Graph the function. $g ( x ) = \frac { 1 } { 4 } ( x - 2 ) ^ { 2 } - 4$