Question 1

Solve.
-$$4 r ^ { 2 } + 24 r = - 19$$

Accepted Answer

A)  $\frac { - 24 \pm \sqrt { 17 } } { 2 }$ 
B)  $\frac { - 6 \pm \sqrt { 55 } } { 2 }$ 
C)  $\frac { - 6 \pm \sqrt { 17 } } { 2 }$ 
D)  $\frac { - 6 \pm \sqrt { 17 } } { 8 }$ 
A)  $\frac { - 24 \pm \sqrt { 17 } } { 2 }$ 
B)  $\frac { - 6 \pm \sqrt { 55 } } { 2 }$ 
C)  $\frac { - 6 \pm \sqrt { 17 } } { 2 }$ 
D)  $\frac { - 6 \pm \sqrt { 17 } } { 8 }$

Question 2

Solve the equation by completing the square.
-$$x ^ { 2 } - 12 x + 45 = 0$$

Accepted Answer

A)  $- 6 \pm 3 i$ 
B)  9,3 
C)  $12 \pm 6 i$ 
D)  $6 \pm 3 \mathrm { i }$ 
A)  $- 6 \pm 3 i$ 
B)  9,3 
C)  $12 \pm 6 i$ 
D)  $6 \pm 3 \mathrm { i }$

Question 3

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

Accepted Answer

A)  $x$-intercepts $( 0,0 )$ and $( 7,0 )$ 
B)  x-intercepts $( 0 , - 7 )$ and $( - 7,0 )$ 
C)  No x-intercept 
D)  $x$-intercepts $( 0,0 )$ and $( - 7,0 )$ 
A)  $x$-intercepts $( 0,0 )$ and $( 7,0 )$ 
B)  x-intercepts $( 0 , - 7 )$ and $( - 7,0 )$ 
C)  No x-intercept 
D)  $x$-intercepts $( 0,0 )$ and $( - 7,0 )$

Question 4

Solve.
-$$x ^ { 2 } + x + 7 = 0$$

Accepted Answer

A)  $- \frac { 1 } { 2 } \pm \frac { 3 \sqrt { 3 } } { 2 }$ 
B)  $\frac { 1 } { 2 } \pm \frac { 3 \sqrt { 3 } } { 2 }$ 
C)  $- \frac { 1 } { 2 } \pm \frac { 3 \sqrt { 3 } } { 2 } \mathrm { i }$ 
D)  $\frac { 1 } { 2 } \pm \frac { 3 \sqrt { 3 } } { 2 } \mathrm { i }$ 
A)  $- \frac { 1 } { 2 } \pm \frac { 3 \sqrt { 3 } } { 2 }$ 
B)  $\frac { 1 } { 2 } \pm \frac { 3 \sqrt { 3 } } { 2 }$ 
C)  $- \frac { 1 } { 2 } \pm \frac { 3 \sqrt { 3 } } { 2 } \mathrm { i }$ 
D)  $\frac { 1 } { 2 } \pm \frac { 3 \sqrt { 3 } } { 2 } \mathrm { i }$

Question 5

Find the x-intercepts.
-$$f ( x ) = - x ^ { 2 } + 19 x - 90$$

Accepted Answer

A)  $x$-intercepts $( 9,0 )$ and $( - 10,0 )$ 
B)  $x$-intercepts $( - 9,0 )$ and $( - 10,0 )$ 
C)  No x-intercepts 
D)  $x$-intercepts $( 9,0 )$ and $( 10,0 )$ 
A)  $x$-intercepts $( 9,0 )$ and $( - 10,0 )$ 
B)  $x$-intercepts $( - 9,0 )$ and $( - 10,0 )$ 
C)  No x-intercepts 
D)  $x$-intercepts $( 9,0 )$ and $( 10,0 )$

Question 6

Solve the problem. Give the answer to the nearest tenth.
-A ball is thrown downward from a window in a tall building. Its position at time $t$ in seconds is s $= 16 t ^ { 2 } + 32 t$, where $s$ is in feet. How long (to the nearest tenth) will it take the ball to fall 54 feet?

Accepted Answer

A)  $1.2 \mathrm { sec }$ 
B)  $1.1 \mathrm { sec }$ 
C)  $0.9 \mathrm { sec }$ 
D)  $1.8 \mathrm { sec }$ 
A)  $1.2 \mathrm { sec }$ 
B)  $1.1 \mathrm { sec }$ 
C)  $0.9 \mathrm { sec }$ 
D)  $1.8 \mathrm { sec }$

Question 7

Solve. Round results to the nearest thousandth.
-$3 y ^ { 2 } - 4 y = 1$

Accepted Answer

A)  $1.000,0.333$ 
B)  $0.215 , - 1.549$ 
C)  $1.549 , - 0.215$ 
D)  $3.098 , - 0.430$ 
A)  $1.000,0.333$ 
B)  $0.215 , - 1.549$ 
C)  $1.549 , - 0.215$ 
D)  $3.098 , - 0.430$

Question 8

Solve. Give exact solutions.
-$$( x + 9 ) ^ { 2 } - 3 = 0$$

Accepted Answer

A)  $- 6,12$ 
B)  $9 \pm \sqrt { 3 }$ 
C)  $- 9 \pm \sqrt { 3 }$ 
D)  $- 3 \pm \sqrt { 3 }$ 
A)  $- 6,12$ 
B)  $9 \pm \sqrt { 3 }$ 
C)  $- 9 \pm \sqrt { 3 }$ 
D)  $- 3 \pm \sqrt { 3 }$

Question 9

Find the x-intercepts.
-$$f ( x ) = 3 x ^ { 2 } + 3 x - 5$$

Accepted Answer

A)  $\left( \frac { - 3 + \sqrt { 69 } } { 6 } , 0 \right)$ and $\left( \frac { - 3 - \sqrt { 69 } } { 6 } , 0 \right)$ 
B)  $\left( \frac { 3 + \sqrt { 69 } } { 6 } , 0 \right)$ and $\left( \frac { 3 - \sqrt { 69 } } { 6 } , 0 \right)$ 
C)  $\left( \frac { 3 + \sqrt { 51 } } { 6 } , 0 \right)$ and $\left( \frac { 3 - \sqrt { 51 } } { 6 } , 0 \right)$ 
D)  $\left( \frac { - 3 + \sqrt { 51 } } { 6 } , 0 \right)$ and $\left( \frac { - 3 - \sqrt { 51 } } { 6 } , 0 \right)$ 
A)  $\left( \frac { - 3 + \sqrt { 69 } } { 6 } , 0 \right)$ and $\left( \frac { - 3 - \sqrt { 69 } } { 6 } , 0 \right)$ 
B)  $\left( \frac { 3 + \sqrt { 69 } } { 6 } , 0 \right)$ and $\left( \frac { 3 - \sqrt { 69 } } { 6 } , 0 \right)$ 
C)  $\left( \frac { 3 + \sqrt { 51 } } { 6 } , 0 \right)$ and $\left( \frac { 3 - \sqrt { 51 } } { 6 } , 0 \right)$ 
D)  $\left( \frac { - 3 + \sqrt { 51 } } { 6 } , 0 \right)$ and $\left( \frac { - 3 - \sqrt { 51 } } { 6 } , 0 \right)$

Question 10

Find the x-intercepts.
-$$f ( x ) = x ^ { 2 } - 10$$

Accepted Answer

A)  x-intercepts $( 0,10 )$ and $( 0 , - 10 )$ 
B)  $x$-intercepts $( 0 , \sqrt { 10 } )$ and $( 0 , - \sqrt { 10 } )$ 
C)  No x-intercepts 
D)  $x$-intercepts $( \sqrt { 10 } , 0 )$ and $( - \sqrt { 10 } , 0 )$ 
A)  x-intercepts $( 0,10 )$ and $( 0 , - 10 )$ 
B)  $x$-intercepts $( 0 , \sqrt { 10 } )$ and $( 0 , - \sqrt { 10 } )$ 
C)  No x-intercepts 
D)  $x$-intercepts $( \sqrt { 10 } , 0 )$ and $( - \sqrt { 10 } , 0 )$

Question 11

Solve.
-Sue rowed her boat across Lake Bend and back in 3 hours. If her rate returning was 2 mph less than the rate going, and if the distance each way was 7 miles, find her rate going.

Accepted Answer

A) 5.5 mph 
B) 5.9 mph 
C) 1.5 mph 
D) 3.7 mph 
A) 5.5 mph 
B) 5.9 mph 
C) 1.5 mph 
D) 3.7 mph

Question 12

Solve.
-$$7 x ^ { 2 } = - 12 x - 2$$

Accepted Answer

A)  $\frac { - 6 \pm \sqrt { 2 } } { 7 }$ 
B)  $\frac { - 6 \pm \sqrt { 22 } } { 7 }$ 
C)  $\frac { - 6 \pm \sqrt { 22 } } { 14 }$ 
D)  $\frac { - 12 \pm \sqrt { 22 } } { 7 }$ 
A)  $\frac { - 6 \pm \sqrt { 2 } } { 7 }$ 
B)  $\frac { - 6 \pm \sqrt { 22 } } { 7 }$ 
C)  $\frac { - 6 \pm \sqrt { 22 } } { 14 }$ 
D)  $\frac { - 12 \pm \sqrt { 22 } } { 7 }$

Question 13

Solve the problem. Give the answer to the nearest tenth.
-The position of an object moving in a straight line is given by $s = 2 t ^ { 2 } - 3 t$, where $s$ is in meters and $t$ is the time in seconds the object has been in motion. How long (to the nearest tenth) will it take the object to move 19 meters?

Accepted Answer

A)  $3.9 \mathrm { sec }$ 
B)  $3.7 \mathrm { sec }$ 
C)  $20.0 \mathrm { sec }$ 
D)  $66.5 \mathrm { sec }$ 
A)  $3.9 \mathrm { sec }$ 
B)  $3.7 \mathrm { sec }$ 
C)  $20.0 \mathrm { sec }$ 
D)  $66.5 \mathrm { sec }$

Question 14

Solve.
-A rectangular garden has dimensions of 23 feet by 16 feet. A gravel path of equal width is to be built around the garden. How wide can the path be if there is enough gravel for 612 square feet?

Accepted Answer

A) 8.5 ft 
B) 6 ft 
C) 8 ft 
D) 7 ft 
A) 8.5 ft 
B) 6 ft 
C) 8 ft 
D) 7 ft

Question 15

Solve.
-A man rode a bicycle for 12 miles and then hiked an additional 8 miles. The total time for the trip was 5 hours. If his rate when he was riding a bicycle was 10 miles per hour faster than his rate walking, what was each rate?

Accepted Answer

A) Bike: 12 mph 
B) Bike: 14.5 mph 
C) Bike: 11.5 mph 
D) Bike: 13 mph Hike: 2 mph Hike: 4.5 mph Hike: 1.5 mph Hike: 3 mph 
A) Bike: 12 mph 
B) Bike: 14.5 mph 
C) Bike: 11.5 mph 
D) Bike: 13 mph Hike: 2 mph Hike: 4.5 mph Hike: 1.5 mph Hike: 3 mph

Question 16

Solve.
-A ladder is resting against a wall. The top of the ladder touches the wall at a height of 6 ft. Find the length of the ladder if the length is 2 ft more than its distance from the wall.

Accepted Answer

A) 8 ft 
B) 6 ft 
C) 10 ft 
D) 12 ft 
A) 8 ft 
B) 6 ft 
C) 10 ft 
D) 12 ft

Question 17

Find the x-intercepts.
-$$f ( x ) = 2 x ^ { 2 } - 20 x + 18$$

Accepted Answer

A)  $x$-intercepts $( 1,0 )$ and $( 9,0 )$ 
B)  $x$-intercepts $( - 1,0 )$ and $( 9,0 )$ 
C)  $x$-intercepts $( - 1,0 )$ and $( - 9,0 )$ 
D)  $x$-intercepts $( 1,0 )$ and $( - 9,0 )$ 
A)  $x$-intercepts $( 1,0 )$ and $( 9,0 )$ 
B)  $x$-intercepts $( - 1,0 )$ and $( 9,0 )$ 
C)  $x$-intercepts $( - 1,0 )$ and $( - 9,0 )$ 
D)  $x$-intercepts $( 1,0 )$ and $( - 9,0 )$

Question 18

Solve the equation by completing the square.
-$$a ^ { 2 } + 4 a + 3 = 0$$

Accepted Answer

A)  $6 , - 3$ 
B)  1,3 
C)  $\sqrt { 3 } , - \sqrt { 3 }$ 
D)  $- 1 , - 3$ 
A)  $6 , - 3$ 
B)  1,3 
C)  $\sqrt { 3 } , - \sqrt { 3 }$ 
D)  $- 1 , - 3$

Question 19

Solve the equation by completing the square.
-$11 \mathrm {~m} ^ { 2 } + 3 \mathrm {~m} = 0$

Accepted Answer

A)  $\frac { 3 } { 11 } , 0$ 
B)  0 
C)  $- \frac { 3 } { 11 } , 0$ 
D)  $\pm \frac { 3 } { 11 }$ 
A)  $\frac { 3 } { 11 } , 0$ 
B)  0 
C)  $- \frac { 3 } { 11 } , 0$ 
D)  $\pm \frac { 3 } { 11 }$

Question 20

Solve by completing the square.
-$$x ^ { 2 } + 3 x - 9 = 0$$

Accepted Answer

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

Solve. - $4 r ^ { 2 } + 24 r = - 19$

Solve the equation by completing the square. - $x ^ { 2 } - 12 x + 45 = 0$

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

Solve. - $x ^ { 2 } + x + 7 = 0$

Find the x-intercepts. - $f ( x ) = - x ^ { 2 } + 19 x - 90$

Solve the problem. Give the answer to the nearest tenth. -A ball is thrown downward from a window in a tall building. Its position at time $t$ in seconds is s $= 16 t ^ { 2 } + 32 t$ , where $s$ is in feet. How long (to the nearest tenth) will it take the ball to fall 54 feet?

Solve. Round results to the nearest thousandth. - $3 y ^ { 2 } - 4 y = 1$

Solve. Give exact solutions. - $( x + 9 ) ^ { 2 } - 3 = 0$

Find the x-intercepts. - $f ( x ) = 3 x ^ { 2 } + 3 x - 5$

Find the x-intercepts. - $f ( x ) = x ^ { 2 } - 10$

Solve. -Sue rowed her boat across Lake Bend and back in 3 hours. If her rate returning was 2 mph less than the rate going, and if the distance each way was 7 miles, find her rate going.

Solve. - $7 x ^ { 2 } = - 12 x - 2$

Solve. -A rectangular garden has dimensions of 23 feet by 16 feet. A gravel path of equal width is to be built around the garden. How wide can the path be if there is enough gravel for 612 square feet?

Solve. -A man rode a bicycle for 12 miles and then hiked an additional 8 miles. The total time for the trip was 5 hours. If his rate when he was riding a bicycle was 10 miles per hour faster than his rate walking, what was each rate?

Solve. -A ladder is resting against a wall. The top of the ladder touches the wall at a height of 6 ft. Find the length of the ladder if the length is 2 ft more than its distance from the wall.

Find the x-intercepts. - $f ( x ) = 2 x ^ { 2 } - 20 x + 18$

Solve the equation by completing the square. - $a ^ { 2 } + 4 a + 3 = 0$

Solve the equation by completing the square. - $11 \mathrm {~m} ^ { 2 } + 3 \mathrm {~m} = 0$

Solve by completing the square. - $x ^ { 2 } + 3 x - 9 = 0$

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

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Exponential Functions and Logarithmic Functions

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Exam 11: Quadratic Equations and Functions

Solve. - 4r2+24r=−194 r ^ { 2 } + 24 r = - 194r2+24r=−19

Solve the equation by completing the square. - x2−12x+45=0x ^ { 2 } - 12 x + 45 = 0x2−12x+45=0

Find the x-intercepts. - f(x)=x2+7xf( x ) = x ^ { 2 } + 7 xf(x)=x2+7x

Solve. - x2+x+7=0x ^ { 2 } + x + 7 = 0x2+x+7=0

Find the x-intercepts. - f(x)=−x2+19x−90f ( x ) = - x ^ { 2 } + 19 x - 90f(x)=−x2+19x−90

Solve the problem. Give the answer to the nearest tenth. -A ball is thrown downward from a window in a tall building. Its position at time ttt in seconds is s =16t2+32t= 16 t ^ { 2 } + 32 t=16t2+32t , where sss is in feet. How long (to the nearest tenth) will it take the ball to fall 54 feet?

Solve. Round results to the nearest thousandth. - 3y2−4y=13 y ^ { 2 } - 4 y = 13y2−4y=1

Solve. Give exact solutions. - (x+9)2−3=0( x + 9 ) ^ { 2 } - 3 = 0(x+9)2−3=0

Find the x-intercepts. - f(x)=3x2+3x−5f ( x ) = 3 x ^ { 2 } + 3 x - 5f(x)=3x2+3x−5

Find the x-intercepts. - f(x)=x2−10f ( x ) = x ^ { 2 } - 10f(x)=x2−10