Question 1

Solve by completing the square.
-$$\mathrm { q } ^ { 2 } + 4 \mathrm { q } - 9 = 0$$

Accepted Answer

A)  $2 + \sqrt { 13 }$ 
B)  $- 2 \pm \sqrt { 13 }$ 
C)  $- 1 \pm \sqrt { 13 }$ 
D)  $- 2 \pm 2 \sqrt { 13 }$ 
A)  $2 + \sqrt { 13 }$ 
B)  $- 2 \pm \sqrt { 13 }$ 
C)  $- 1 \pm \sqrt { 13 }$ 
D)  $- 2 \pm 2 \sqrt { 13 }$

Question 2

Solve.
-$41 m ^ { 2 } + 100 m + 53 = 0$

Accepted Answer

A)  $\frac { - 50 \pm \sqrt { 4673 } } { 41 }$ 
B)  $\frac { - 50 \pm \sqrt { 327 } } { 82 }$ 
C)  $\frac { - 100 \pm \sqrt { 327 } } { 41 }$ 
D)  $\frac { - 50 \pm \sqrt { 327 } } { 41 }$ 
A)  $\frac { - 50 \pm \sqrt { 4673 } } { 41 }$ 
B)  $\frac { - 50 \pm \sqrt { 327 } } { 82 }$ 
C)  $\frac { - 100 \pm \sqrt { 327 } } { 41 }$ 
D)  $\frac { - 50 \pm \sqrt { 327 } } { 41 }$

Question 3

Solve. Give exact solutions.
-$$x ^ { 2 } = 16$$

Accepted Answer

A)  8 
B)  $\pm 5$ 
C)  4 
D)  $\pm 4$ 
A)  8 
B)  $\pm 5$ 
C)  4 
D)  $\pm 4$

Question 4

Find the x-intercepts.
-$$f ( x ) = 2 x ^ { 2 } - 12 x - 54$$

Accepted Answer

A)  $x$-intercepts $( 9,0 )$ and $( 3,0 )$ 
B)  $x$-intercepts $( 9,0 )$ and $( - 3,0 )$ 
C)  No x-intercepts 
D)  $x$-intercepts $( - 6,0 )$ and $\left( \frac { 9 } { 2 } , 0 \right)$ 
A)  $x$-intercepts $( 9,0 )$ and $( 3,0 )$ 
B)  $x$-intercepts $( 9,0 )$ and $( - 3,0 )$ 
C)  No x-intercepts 
D)  $x$-intercepts $( - 6,0 )$ and $\left( \frac { 9 } { 2 } , 0 \right)$

Question 5

Solve. Give exact solutions.
-$$4 x ^ { 2 } + 36 = 0$$

Accepted Answer

A)  $\pm 3 i$ 
B)  $3 \pm i$ 
C)  $\pm 3$ 
D)  $\pm 3 + \mathrm { i }$ 
A)  $\pm 3 i$ 
B)  $3 \pm i$ 
C)  $\pm 3$ 
D)  $\pm 3 + \mathrm { i }$

Question 6

Solve the equation by completing the square.
-$$z ^ { 2 } + 10 z + 11 = 0$$

Accepted Answer

A)  $5 \pm \sqrt { 11 }$ 
B)  $- 10 + \sqrt { 11 }$ 
C)  $- 5 \pm \sqrt { 14 }$ 
D)  $5 + \sqrt { 14 }$ 
A)  $5 \pm \sqrt { 11 }$ 
B)  $- 10 + \sqrt { 11 }$ 
C)  $- 5 \pm \sqrt { 14 }$ 
D)  $5 + \sqrt { 14 }$

Question 7

Solve. Give exact solutions.
-$$( x + 4 ) ^ { 2 } - 6 = 0$$

Accepted Answer

A)  $- 4 + \sqrt { 6 } , - 4 - \sqrt { 6 }$ 
B)  $- 2 + \sqrt { 6 } , - 2 - \sqrt { 6 }$ 
C)  $- 4 + i \sqrt { 6 } , - 4 - i \sqrt { 6 }$ 
D)  2,10 
A)  $- 4 + \sqrt { 6 } , - 4 - \sqrt { 6 }$ 
B)  $- 2 + \sqrt { 6 } , - 2 - \sqrt { 6 }$ 
C)  $- 4 + i \sqrt { 6 } , - 4 - i \sqrt { 6 }$ 
D)  2,10

Question 8

Solve.
-A jet plane traveling at a constant speed goes 1200 miles with the wind, then turns around and travels for 1000 miles against the wind. If the speed of the wind is 50 mph and the total flight took 4 hours, find the speed of the Plane in still air.

Accepted Answer

A) 435 mph 
B) 550 mph 
C) 605 mph 
D) 525 mph 
A) 435 mph 
B) 550 mph 
C) 605 mph 
D) 525 mph

Question 9

Solve.
-$$3 m ^ { 2 } + 12 m + 5 = 0$$

Accepted Answer

A)  $\frac { - 6 \pm \sqrt { 51 } } { 3 }$ 
B)  $\frac { - 6 \pm \sqrt { 21 } } { 3 }$ 
C)  $\frac { - 12 \pm \sqrt { 21 } } { 3 }$ 
D)  $\frac { - 6 \pm \sqrt { 21 } } { 6 }$ 
A)  $\frac { - 6 \pm \sqrt { 51 } } { 3 }$ 
B)  $\frac { - 6 \pm \sqrt { 21 } } { 3 }$ 
C)  $\frac { - 12 \pm \sqrt { 21 } } { 3 }$ 
D)  $\frac { - 6 \pm \sqrt { 21 } } { 6 }$

Question 10

Solve.
-A rug is to fit in a room so that a border of even width is left on all four sides. If the room is 18 feet by 20 feet and the area of the rug is 120 square feet, how wide will the border be?

Accepted Answer

A) 6 ft 
B) 5 ft 
C) 6.5 ft 
D) 4 ft 
A) 6 ft 
B) 5 ft 
C) 6.5 ft 
D) 4 ft

Question 11

Solve. Give exact solutions.
-$$( x - 4 ) ^ { 2 } = 4$$

Accepted Answer

A)  $2 , - 2$ 
B)  $2 , - 6$ 
C)  6,2 
D)  8 
A)  $2 , - 2$ 
B)  $2 , - 6$ 
C)  6,2 
D)  8

Question 12

Find the x-intercepts.
-$$f ( x ) = 2 x + x ( x - 7 )$$

Accepted Answer

A)  $( 0,0 )$ and $( - 5,0 )$ 
B)  $( 0,0 )$ and $( 5,0 )$ 
C)  $( 5,0 )$ 
D)  $( - 5,0 )$ 
A)  $( 0,0 )$ and $( - 5,0 )$ 
B)  $( 0,0 )$ and $( 5,0 )$ 
C)  $( 5,0 )$ 
D)  $( - 5,0 )$

Question 13

Find the x-intercepts.
-$$f ( x ) = 11 x ^ { 2 } - 3 x - 6$$

Accepted Answer

A)  No x-intercepts 
B)  $( 9,0 )$ and $( 6,0 )$ 
C)  $\left( \frac { 3 + \sqrt { 273 } } { 22 } , 0 \right)$ and $\left( \frac { 3 - \sqrt { 273 } } { 22 } , 0 \right)$ 
D)  $\left( \frac { 3 + \sqrt { 261 } } { 22 } , 0 \right)$ and $\left( \frac { 3 - \sqrt { 261 } } { 22 } , 0 \right)$ 
A)  No x-intercepts 
B)  $( 9,0 )$ and $( 6,0 )$ 
C)  $\left( \frac { 3 + \sqrt { 273 } } { 22 } , 0 \right)$ and $\left( \frac { 3 - \sqrt { 273 } } { 22 } , 0 \right)$ 
D)  $\left( \frac { 3 + \sqrt { 261 } } { 22 } , 0 \right)$ and $\left( \frac { 3 - \sqrt { 261 } } { 22 } , 0 \right)$

Question 14

Solve the formula for the indicated letter. Assume that all variables represent nonnegative numbers.
-$$S = \frac { 1 } { 2 } g t ^ { 2 } \text { for } t$$

Accepted Answer

A)  $t = \sqrt { \frac { g } { 2 S } }$ 
B)  $t = \sqrt { \frac { 2 S } { g } }$ 
C)  $t = 2 \sqrt { g s }$ 
D)  $t = 2 g S$ 
A)  $t = \sqrt { \frac { g } { 2 S } }$ 
B)  $t = \sqrt { \frac { 2 S } { g } }$ 
C)  $t = 2 \sqrt { g s }$ 
D)  $t = 2 g S$

Question 15

Solve the formula for the indicated letter. Assume that all variables represent nonnegative numbers.
-$$v ^ { 2 } = 2 a s \text { for } v$$

Accepted Answer

A)  $v = \sqrt { \frac { 2 a } { s } }$ 
B)  $v = \sqrt { 2 a s }$ 
C)  $v = 2 a \sqrt { s }$ 
D)  $v = \frac { 2 a } { s }$ 
A)  $v = \sqrt { \frac { 2 a } { s } }$ 
B)  $v = \sqrt { 2 a s }$ 
C)  $v = 2 a \sqrt { s }$ 
D)  $v = \frac { 2 a } { s }$

Question 16

Determine the nature of the solutions of the equation.
-$$s ^ { 2 } - 6 s - 7 = 0$$

Accepted Answer

A)  Two nonreal 
B)  Two real 
C)  One real 
A)  Two nonreal 
B)  Two real 
C)  One real

Question 17

Solve by completing the square.
-$$z ^ { 2 } + 4 z - 9 = 0$$

Accepted Answer

A)  $- 2 \pm \sqrt { 13 }$ 
B)  $- 1 \pm \sqrt { 13 }$ 
C)  $- 2 \pm 2 \sqrt { 13 }$ 
D)  $2 + \sqrt { 13 }$ 
A)  $- 2 \pm \sqrt { 13 }$ 
B)  $- 1 \pm \sqrt { 13 }$ 
C)  $- 2 \pm 2 \sqrt { 13 }$ 
D)  $2 + \sqrt { 13 }$

Question 18

Solve.
-$$4 \mathrm { x } ^ { 2 } + 6 \mathrm { x } = - 1$$

Accepted Answer

A)  $\frac { - 3 \pm \sqrt { 5 } } { 4 }$ 
B)  $\frac { - 3 \pm \sqrt { 13 } } { 4 }$ 
C)  $\frac { - 3 \pm \sqrt { 5 } } { 8 }$ 
D)  $\frac { - 6 \pm \sqrt { 5 } } { 4 }$ 
A)  $\frac { - 3 \pm \sqrt { 5 } } { 4 }$ 
B)  $\frac { - 3 \pm \sqrt { 13 } } { 4 }$ 
C)  $\frac { - 3 \pm \sqrt { 5 } } { 8 }$ 
D)  $\frac { - 6 \pm \sqrt { 5 } } { 4 }$

Question 19

Solve.
-$5 x ^ { 2 } - 3 x = - 7$

Accepted Answer

A)  $\frac { 3 } { 10 } \pm \frac { \sqrt { 131 } } { 10 } \mathrm { i }$ 
B)  $- \frac { 3 } { 10 } \pm \frac { \sqrt { 131 } } { 10 }$ 
C)  $\frac { 3 } { 10 } \pm \frac { \sqrt { 131 } } { 10 }$ 
D)  $- \frac { 3 } { 10 } \pm \frac { \sqrt { 131 } } { 10 } \mathrm { i }$ 
A)  $\frac { 3 } { 10 } \pm \frac { \sqrt { 131 } } { 10 } \mathrm { i }$ 
B)  $- \frac { 3 } { 10 } \pm \frac { \sqrt { 131 } } { 10 }$ 
C)  $\frac { 3 } { 10 } \pm \frac { \sqrt { 131 } } { 10 }$ 
D)  $- \frac { 3 } { 10 } \pm \frac { \sqrt { 131 } } { 10 } \mathrm { i }$

Question 20

Solve. Give exact solutions.
-$$( r + 5 ) ^ { 2 } = 14$$

Accepted Answer

A)  9 
B)  $- 5 + \sqrt { 14 } , - 5 - \sqrt { 14 }$ 
C)  $\sqrt { 14 } , \sqrt { 14 }$ 
D)  $5 + \sqrt { 14 } , 5 - \sqrt { 14 }$ 
A)  9 
B)  $- 5 + \sqrt { 14 } , - 5 - \sqrt { 14 }$ 
C)  $\sqrt { 14 } , \sqrt { 14 }$ 
D)  $5 + \sqrt { 14 } , 5 - \sqrt { 14 }$

Solve by completing the square. - $\mathrm { q } ^ { 2 } + 4 \mathrm { q } - 9 = 0$

Solve. - $41 m ^ { 2 } + 100 m + 53 = 0$

Solve. Give exact solutions. - $x ^ { 2 } = 16$

Find the x-intercepts. - $f ( x ) = 2 x ^ { 2 } - 12 x - 54$

Solve. Give exact solutions. - $4 x ^ { 2 } + 36 = 0$

Solve the equation by completing the square. - $z ^ { 2 } + 10 z + 11 = 0$

Solve. Give exact solutions. - $( x + 4 ) ^ { 2 } - 6 = 0$

Solve. -A jet plane traveling at a constant speed goes 1200 miles with the wind, then turns around and travels for 1000 miles against the wind. If the speed of the wind is 50 mph and the total flight took 4 hours, find the speed of the Plane in still air.

Solve. - $3 m ^ { 2 } + 12 m + 5 = 0$

Solve. -A rug is to fit in a room so that a border of even width is left on all four sides. If the room is 18 feet by 20 feet and the area of the rug is 120 square feet, how wide will the border be?

Solve. Give exact solutions. - $( x - 4 ) ^ { 2 } = 4$

Find the x-intercepts. - $f ( x ) = 2 x + x ( x - 7 )$

Find the x-intercepts. - $f ( x ) = 11 x ^ { 2 } - 3 x - 6$

Solve the formula for the indicated letter. Assume that all variables represent nonnegative numbers. - $S = \frac { 1 } { 2 } g t ^ { 2 } \text { for } t$

Solve the formula for the indicated letter. Assume that all variables represent nonnegative numbers. - $v ^ { 2 } = 2 a s \text { for } v$

Determine the nature of the solutions of the equation. - $s ^ { 2 } - 6 s - 7 = 0$

Solve by completing the square. - $z ^ { 2 } + 4 z - 9 = 0$

Solve. - $4 \mathrm { x } ^ { 2 } + 6 \mathrm { x } = - 1$

Solve. - $5 x ^ { 2 } - 3 x = - 7$

Solve. Give exact solutions. - $( r + 5 ) ^ { 2 } = 14$

Introduction to Real Numbers and Algebraic Expressions

Solving Equations and Inequalities

Graphs of Linear Equations

Polynomials: Operations

Polynomials: Factoring

Rational Expressions and Equations

Graphs, Functions, and Applications

Systems of Equations

More on Inequalities

Radical Expressions, Equations, and Functions

Exponential Functions and Logarithmic Functions

Filters

Exam 11: Quadratic Equations and Functions

Solve by completing the square. - q2+4q−9=0\mathrm { q } ^ { 2 } + 4 \mathrm { q } - 9 = 0q2+4q−9=0

Solve. - 41m2+100m+53=041 m ^ { 2 } + 100 m + 53 = 041m2+100m+53=0

Solve. Give exact solutions. - x2=16x ^ { 2 } = 16x2=16

Find the x-intercepts. - f(x)=2x2−12x−54f ( x ) = 2 x ^ { 2 } - 12 x - 54f(x)=2x2−12x−54

Solve. Give exact solutions. - 4x2+36=04 x ^ { 2 } + 36 = 04x2+36=0

Solve the equation by completing the square. - z2+10z+11=0z ^ { 2 } + 10 z + 11 = 0z2+10z+11=0

Solve. Give exact solutions. - (x+4)2−6=0( x + 4 ) ^ { 2 } - 6 = 0(x+4)2−6=0