Question 1

Solve the quadratic equation by completing the square and applying the square root property. $$k ^ { 2 } + 14 k + 50 = 0$$

Accepted Answer

A)  $\{ - 7 \pm i \}$ 
B)  $\{ \pm i \}$ 
C)  $\{ - 7 + i \}$ 
D)  $\{ 7 + i \}$ 
A)  $\{ - 7 \pm i \}$ 
B)  $\{ \pm i \}$ 
C)  $\{ - 7 + i \}$ 
D)  $\{ 7 + i \}$

Question 2

Solve the equation by using the quadratic formula. $$6 - 4 t ^ { 2 } = 0$$

Accepted Answer

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

Question 3

Use the discriminant to determine the type and number of solutions. x(2x + 11) = 40

Accepted Answer

A)  Two imaginary solutions 
B)  Two rational solutions 
C)  Two irrational solutions 
D)  One rational solution 
A)  Two imaginary solutions 
B)  Two rational solutions 
C)  Two irrational solutions 
D)  One rational solution

Question 4

Solve the polynomial inequality. Write the answer in interval notation. $$- y ^ { 2 } + 17 > - 2 y$$

Accepted Answer

A)  $( - \infty , 2 - \sqrt { 3 } ) \cup ( 2 + \sqrt { 3 } , \infty )$ 
B)  $( 1 - 3 \sqrt { 2 } , 1 + 3 \sqrt { 2 } )$ 
C)  $( 2 - \sqrt { 3 } , 2 + \sqrt { 3 } )$ 
D)  {  } 
A)  $( - \infty , 2 - \sqrt { 3 } ) \cup ( 2 + \sqrt { 3 } , \infty )$ 
B)  $( 1 - 3 \sqrt { 2 } , 1 + 3 \sqrt { 2 } )$ 
C)  $( 2 - \sqrt { 3 } , 2 + \sqrt { 3 } )$ 
D)  {  }

Question 5

Solve for $t$.
$$a t ^ { 2 } + c z = b$$

Accepted Answer

The answer of Solve for $t$.
\[a t ^ { 2...

Question 6

Solve the inequality. $$- 4 y ^ { 2 } - 6 > - 2 y$$

Accepted Answer

The answer of Solve the inequality. \[- 4 y ^...

Question 7

Write the coordinates of the vertex and determine if the vertex is a maximum point or a minimum point. $$f ( x ) = ( x + 12 ) ^ { 2 } - 8$$

Accepted Answer

A)  (-12, -8); maximum 
B)  (-8, 12); maximum 
C)  (12, -8); minimum 
D)  (-12, -8); minimum 
A)  (-12, -8); maximum 
B)  (-8, 12); maximum 
C)  (12, -8); minimum 
D)  (-12, -8); minimum

Question 8

The temperature at a state park for one day in June can be approximated by the function $T ( x ) = 0.284 x ^ { 2 } - 5.11 x + 82 \quad 0 \leq x \leq 18$ where T is degrees Fahrenheit and x is the number of hours after 5 PM on Friday. At what time is the temperature lowest? Round to the nearest hour.

Accepted Answer

A)  2 AM 
B)  9 AM 
C)  11 PM 
D)  5 PM 
A)  2 AM 
B)  9 AM 
C)  11 PM 
D)  5 PM

Question 9

Solve the equation by using substitution. $$( t + 8 ) ^ { 2 } - ( t + 8 ) - 12 = 0$$

Accepted Answer

A)  {4, 11} 
B)  {-4, -11} 
C)  {-12, -5} 
D)  {4, -3} 
A)  {4, 11} 
B)  {-4, -11} 
C)  {-12, -5} 
D)  {4, -3}

Question 10

Solve the quadratic equation by completing the square and applying the square root property. $$7 - 3 t = 2 t ^ { 2 }$$

Accepted Answer

The answer of Solve the quadratic equation by completing the...

Question 11

Solve the equation by using the square root property. $$h ^ { 2 } = 49$$

Accepted Answer

A)  {7} 
B)  {±7} 
C)  {7i} 
D)  {±7i} 
A)  {7} 
B)  {±7} 
C)  {7i} 
D)  {±7i}

Question 12

Find the discriminant and use it to determine the number and type of solutions. $5 j ^ { 2 } = 3$

Accepted Answer

A)  60: Two imaginary solutions 
B)  -60: One rational solutions 
C)  60: Two irrational solutions 
D)  -60: Two imaginary solutions 
A)  60: Two imaginary solutions 
B)  -60: One rational solutions 
C)  60: Two irrational solutions 
D)  -60: Two imaginary solutions

Question 13

Solve the equation by using substitution. $$( 2 y + 4 ) ^ { 2 } = 4 ( 2 y + 4 ) + 7$$

Accepted Answer

The answer of Solve the equation by using substitution. \[(...

Question 14

A model rocket is launched from a raised platform at a speed of 144 feet per second. Its height in feet is given by $h ( t ) = - 16 t ^ { 2 } + 144 t + 20$ (t = seconds after launch). After how many seconds does the object reach its maximum height?

Accepted Answer

A)  2.25 seconds 
B)  20 seconds 
C)  4.5 seconds 
D)  6.5 seconds 
A)  2.25 seconds 
B)  20 seconds 
C)  4.5 seconds 
D)  6.5 seconds

Question 15

Solve the polynomial inequality. Write the answer in interval notation. $$2 x ^ { 2 } - 17 x \leq - 21$$

Accepted Answer

A)  $\left[ \frac { 3 } { 2 } , 7 \right]$ 
B)  $\left( - \infty , \frac { 3 } { 2 } \right) \cup ( 7 , \infty )$ 
C)  $\left[ - 7 , - \frac { 3 } { 2 } \right]$ 
D) {  } 
A)  $\left[ \frac { 3 } { 2 } , 7 \right]$ 
B)  $\left( - \infty , \frac { 3 } { 2 } \right) \cup ( 7 , \infty )$ 
C)  $\left[ - 7 , - \frac { 3 } { 2 } \right]$ 
D) {  }

Question 16

Solve the quadratic equation by completing the square and applying the square root property. $$y ^ { 2 } + 12 y - 1 = 0$$

Accepted Answer

A)  $\{ - 6 + \sqrt { 37 } , - 6 - \sqrt { 37 } \}$ 
B)  $\{ 2 + 2 \sqrt { 5 } , 2 - 2 \sqrt { 5 } \}$ 
C)  $\{ 2 + i \sqrt { 3 } , 2 - i \sqrt { 3 } \}$ 
D)  $\{ - 2 + 2 \sqrt { 5 } , - 2 - 2 \sqrt { 5 } \}$ 
A)  $\{ - 6 + \sqrt { 37 } , - 6 - \sqrt { 37 } \}$ 
B)  $\{ 2 + 2 \sqrt { 5 } , 2 - 2 \sqrt { 5 } \}$ 
C)  $\{ 2 + i \sqrt { 3 } , 2 - i \sqrt { 3 } \}$ 
D)  $\{ - 2 + 2 \sqrt { 5 } , - 2 - 2 \sqrt { 5 } \}$

Question 17

Find the x- and y-intercepts of the function. $$p ( x ) = 3 x ^ { 2 } + 5 x - 3$$

Accepted Answer

A)  $x$-intercepts: none; $y =$ intercept: $( 0 , - 3 )$ 
B)  $x$-intercepts: $\left( \frac { - 5 - \sqrt { 61 } } { 6 } , 0 \right) , \left( \frac { - 5 + \sqrt { 61 } } { 6 } , 0 \right) ; y =$ intercept: $( 0 , - 5 )$ 
C)  $x$-intercepts: $\left( \frac { - 5 - \sqrt { 61 } } { 6 } , 0 \right) , \left( \frac { - 5 + \sqrt { 61 } } { 6 } , 0 \right) ; y = \operatorname { intercept } : ( 0 , - 3 )$ 
D)  $x$-intercepts: none; $y =$ intercept: $( 0,5 )$ 
A)  $x$-intercepts: none; $y =$ intercept: $( 0 , - 3 )$ 
B)  $x$-intercepts: $\left( \frac { - 5 - \sqrt { 61 } } { 6 } , 0 \right) , \left( \frac { - 5 + \sqrt { 61 } } { 6 } , 0 \right) ; y =$ intercept: $( 0 , - 5 )$ 
C)  $x$-intercepts: $\left( \frac { - 5 - \sqrt { 61 } } { 6 } , 0 \right) , \left( \frac { - 5 + \sqrt { 61 } } { 6 } , 0 \right) ; y = \operatorname { intercept } : ( 0 , - 3 )$ 
D)  $x$-intercepts: none; $y =$ intercept: $( 0,5 )$

Question 18

Graph the function. $$f ( x ) = x ^ { 2 } + 4$$

Accepted Answer

The answer of Graph the function. \[f ( x )...

Question 19

Write the coordinates of the vertex and determine if the vertex is a maximum point or a minimum point. $$g ( x ) = - 4 ( x - 3 ) ^ { 2 } + 12$$

Accepted Answer

A)  (3, 12); minimum 
B)  (-3, 12); maximum 
C)  (3, 12); maximum 
D)  (12, 3); minimum 
A)  (3, 12); minimum 
B)  (-3, 12); maximum 
C)  (3, 12); maximum 
D)  (12, 3); minimum

Question 20

Solve the equation by using the quadratic formula. $$7 x ( x - 2 ) = 5$$

Accepted Answer

A)  $\left\{ 1 \pm \frac { 2 \sqrt { 21 } } { 7 } i \right\}$ 
B)  $\left\{ 1 \pm \frac { 2 \sqrt { 21 } } { 7 } \right\}$ 
C)  $\left\{ - 1 + \frac { 2 \sqrt { 21 } } { 7 } i , - 6 + \frac { 2 \sqrt { 21 } } { 7 } i \right\}$ 
D)  $\left\{ - 1 + \frac { 2 \sqrt { 21 } } { 7 } , - 6 + \frac { 2 \sqrt { 21 } } { 7 } \right\}$ 
A)  $\left\{ 1 \pm \frac { 2 \sqrt { 21 } } { 7 } i \right\}$ 
B)  $\left\{ 1 \pm \frac { 2 \sqrt { 21 } } { 7 } \right\}$ 
C)  $\left\{ - 1 + \frac { 2 \sqrt { 21 } } { 7 } i , - 6 + \frac { 2 \sqrt { 21 } } { 7 } i \right\}$ 
D)  $\left\{ - 1 + \frac { 2 \sqrt { 21 } } { 7 } , - 6 + \frac { 2 \sqrt { 21 } } { 7 } \right\}$

Solve the quadratic equation by completing the square and applying the square root property. $k ^ { 2 } + 14 k + 50 = 0$

Solve the equation by using the quadratic formula. $6 - 4 t ^ { 2 } = 0$

Use the discriminant to determine the type and number of solutions. x(2x + 11) = 40

Solve the polynomial inequality. Write the answer in interval notation. $- y ^ { 2 } + 17 > - 2 y$

Solve for $t$ . $a t ^ { 2 } + c z = b$

Solve the inequality. $- 4 y ^ { 2 } - 6 > - 2 y$

Write the coordinates of the vertex and determine if the vertex is a maximum point or a minimum point. $f ( x ) = ( x + 12 ) ^ { 2 } - 8$

The temperature at a state park for one day in June can be approximated by the function $T ( x ) = 0.284 x ^ { 2 } - 5.11 x + 82 \quad 0 \leq x \leq 18$ where T is degrees Fahrenheit and x is the number of hours after 5 PM on Friday. At what time is the temperature lowest? Round to the nearest hour.

Solve the equation by using substitution. $( t + 8 ) ^ { 2 } - ( t + 8 ) - 12 = 0$

Solve the quadratic equation by completing the square and applying the square root property. $7 - 3 t = 2 t ^ { 2 }$

Solve the equation by using the square root property. $h ^ { 2 } = 49$

Find the discriminant and use it to determine the number and type of solutions. $5 j ^ { 2 } = 3$

Solve the equation by using substitution. $( 2 y + 4 ) ^ { 2 } = 4 ( 2 y + 4 ) + 7$

A model rocket is launched from a raised platform at a speed of 144 feet per second. Its height in feet is given by $h ( t ) = - 16 t ^ { 2 } + 144 t + 20$ (t = seconds after launch). After how many seconds does the object reach its maximum height?

Solve the polynomial inequality. Write the answer in interval notation. $2 x ^ { 2 } - 17 x \leq - 21$

Solve the quadratic equation by completing the square and applying the square root property. $y ^ { 2 } + 12 y - 1 = 0$

Find the x- and y-intercepts of the function. $p ( x ) = 3 x ^ { 2 } + 5 x - 3$

Graph the function. $f ( x ) = x ^ { 2 } + 4$

Write the coordinates of the vertex and determine if the vertex is a maximum point or a minimum point. $g ( x ) = - 4 ( x - 3 ) ^ { 2 } + 12$

Solve the equation by using the quadratic formula. $7 x ( x - 2 ) = 5$

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

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Exam 7: Quadratic Equations, Functions and Inequalities

Solve the quadratic equation by completing the square and applying the square root property. k2+14k+50=0k ^ { 2 } + 14 k + 50 = 0k2+14k+50=0

Solve the equation by using the quadratic formula. 6−4t2=06 - 4 t ^ { 2 } = 06−4t2=0

Use the discriminant to determine the type and number of solutions. x(2x + 11) = 40

Solve the polynomial inequality. Write the answer in interval notation. −y2+17>−2y- y ^ { 2 } + 17 > - 2 y−y2+17>−2y

Solve for ttt . at2+cz=ba t ^ { 2 } + c z = bat2+cz=b

Solve the inequality. −4y2−6>−2y- 4 y ^ { 2 } - 6 > - 2 y−4y2−6>−2y

Write the coordinates of the vertex and determine if the vertex is a maximum point or a minimum point. f(x)=(x+12)2−8f ( x ) = ( x + 12 ) ^ { 2 } - 8f(x)=(x+12)2−8

Solve the equation by using substitution. (t+8)2−(t+8)−12=0( t + 8 ) ^ { 2 } - ( t + 8 ) - 12 = 0(t+8)2−(t+8)−12=0

Solve the quadratic equation by completing the square and applying the square root property. 7−3t=2t27 - 3 t = 2 t ^ { 2 }7−3t=2t2

Solve the equation by using the square root property. h2=49h ^ { 2 } = 49h2=49

Find the discriminant and use it to determine the number and type of solutions. 5j2=35 j ^ { 2 } = 35j2=3

Solve the equation by using substitution. (2y+4)2=4(2y+4)+7( 2 y + 4 ) ^ { 2 } = 4 ( 2 y + 4 ) + 7(2y+4)2=4(2y+4)+7

A model rocket is launched from a raised platform at a speed of 144 feet per second. Its height in feet is given by h(t)=−16t2+144t+20h ( t ) = - 16 t ^ { 2 } + 144 t + 20h(t)=−16t2+144t+20 (t = seconds after launch). After how many seconds does the object reach its maximum height?

Solve the polynomial inequality. Write the answer in interval notation. 2x2−17x≤−212 x ^ { 2 } - 17 x \leq - 212x2−17x≤−21

Solve the quadratic equation by completing the square and applying the square root property. y2+12y−1=0y ^ { 2 } + 12 y - 1 = 0y2+12y−1=0

Find the x- and y-intercepts of the function. p(x)=3x2+5x−3p ( x ) = 3 x ^ { 2 } + 5 x - 3p(x)=3x2+5x−3

Graph the function. f(x)=x2+4f ( x ) = x ^ { 2 } + 4f(x)=x2+4

Write the coordinates of the vertex and determine if the vertex is a maximum point or a minimum point. g(x)=−4(x−3)2+12g ( x ) = - 4 ( x - 3 ) ^ { 2 } + 12g(x)=−4(x−3)2+12

Solve the equation by using the quadratic formula. 7x(x−2)=57 x ( x - 2 ) = 57x(x−2)=5

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

Filters

Solve the quadratic equation by completing the square and applying the square root property. $k ^ { 2 } + 14 k + 50 = 0$

Solve the equation by using the quadratic formula. $6 - 4 t ^ { 2 } = 0$

Solve the polynomial inequality. Write the answer in interval notation. $- y ^ { 2 } + 17 > - 2 y$

Solve for $t$ . $a t ^ { 2 } + c z = b$

Solve the inequality. $- 4 y ^ { 2 } - 6 > - 2 y$

Write the coordinates of the vertex and determine if the vertex is a maximum point or a minimum point. $f ( x ) = ( x + 12 ) ^ { 2 } - 8$

Solve the equation by using substitution. $( t + 8 ) ^ { 2 } - ( t + 8 ) - 12 = 0$

Solve the quadratic equation by completing the square and applying the square root property. $7 - 3 t = 2 t ^ { 2 }$

Solve the equation by using the square root property. $h ^ { 2 } = 49$

Find the discriminant and use it to determine the number and type of solutions. $5 j ^ { 2 } = 3$

Solve the equation by using substitution. $( 2 y + 4 ) ^ { 2 } = 4 ( 2 y + 4 ) + 7$

A model rocket is launched from a raised platform at a speed of 144 feet per second. Its height in feet is given by $h ( t ) = - 16 t ^ { 2 } + 144 t + 20$ (t = seconds after launch). After how many seconds does the object reach its maximum height?

Solve the polynomial inequality. Write the answer in interval notation. $2 x ^ { 2 } - 17 x \leq - 21$

Solve the quadratic equation by completing the square and applying the square root property. $y ^ { 2 } + 12 y - 1 = 0$

Find the x- and y-intercepts of the function. $p ( x ) = 3 x ^ { 2 } + 5 x - 3$

Graph the function. $f ( x ) = x ^ { 2 } + 4$

Write the coordinates of the vertex and determine if the vertex is a maximum point or a minimum point. $g ( x ) = - 4 ( x - 3 ) ^ { 2 } + 12$

Solve the equation by using the quadratic formula. $7 x ( x - 2 ) = 5$