Question 1

Solve. Give exact solutions.
-$- 7 \mathrm { k } ^ { 2 } - 11 = - 123$

Accepted Answer

A)  $- 61.5$ 
B)  $\pm 4$ 
C)  4 
D)  $\pm 8$ 
A)  $- 61.5$ 
B)  $\pm 4$ 
C)  4 
D)  $\pm 8$

Question 2

Find the x-intercepts.
-$$f ( x ) = 64 x ^ { 2 } - 32 x + 4$$

Accepted Answer

A)  No x-intercepts 
B)  $\left( - \frac { 1 } { 4 } , 0 \right)$ 
C)  $\left( \frac { 1 } { 4 } , 0 \right)$ and $\left( - \frac { 1 } { 4 } , 0 \right)$ 
D)  $\left( \frac { 1 } { 4 } , 0 \right)$ 
A)  No x-intercepts 
B)  $\left( - \frac { 1 } { 4 } , 0 \right)$ 
C)  $\left( \frac { 1 } { 4 } , 0 \right)$ and $\left( - \frac { 1 } { 4 } , 0 \right)$ 
D)  $\left( \frac { 1 } { 4 } , 0 \right)$

Question 3

Solve.
-Two cars leave an intersection. One car travels north; the other east. When the car traveling north had gone 15 mi, the distance between the cars was 5 mi more than the distance traveled by the car heading east. How far had
The eastbound car traveled?

Accepted Answer

A) 15 mi 
B) 30 mi 
C) 20 mi 
D) 25 mi 
A) 15 mi 
B) 30 mi 
C) 20 mi 
D) 25 mi

Question 4

Find the x-intercepts.
-$$f ( x ) = - x ^ { 2 } + 17 x - 72$$

Accepted Answer

A)  $x$-intercepts $( - 8,0 )$ and $( - 9,0 )$ 
B)  $x$-intercepts $( 8,0 )$ and $( 9,0 )$ 
C)  No $x$-intercepts 
D)  $x$-intercepts $( 8,0 )$ and $( - 9,0 )$ 
A)  $x$-intercepts $( - 8,0 )$ and $( - 9,0 )$ 
B)  $x$-intercepts $( 8,0 )$ and $( 9,0 )$ 
C)  No $x$-intercepts 
D)  $x$-intercepts $( 8,0 )$ and $( - 9,0 )$

Question 5

Solve by completing the square.
-$$\mathrm { y } ^ { 2 } + 4 \mathrm { y } - 3 = 0$$

Accepted Answer

A)  $- 1 \pm \sqrt { 7 }$ 
B)  $- 2 \pm 2 \sqrt { 7 }$ 
C)  $- 2 \pm \sqrt { 7 }$ 
D)  $2 + \sqrt { 7 }$ 
A)  $- 1 \pm \sqrt { 7 }$ 
B)  $- 2 \pm 2 \sqrt { 7 }$ 
C)  $- 2 \pm \sqrt { 7 }$ 
D)  $2 + \sqrt { 7 }$

Question 6

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

Accepted Answer

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

Question 7

Find the x-intercepts.
-$$f ( x ) = 3 x + x ( x - 5 )$$

Accepted Answer

A)  $( 0,0 )$ and $( 2,0 )$ 
B)  $( - 2,0 )$ 
C)  $( 0,0 )$ and $( - 2,0 )$ 
D)  $( 2,0 )$ 
A)  $( 0,0 )$ and $( 2,0 )$ 
B)  $( - 2,0 )$ 
C)  $( 0,0 )$ and $( - 2,0 )$ 
D)  $( 2,0 )$

Question 8

Solve. Round results to the nearest thousandth.
-$$3 x ^ { 2 } - 6 x = 2$$

Accepted Answer

A)  $0.291 , - 2.291$ 
B)  $2.291 , - 0.291$ 
C)  $4.582 , - 0.582$ 
D)  $1.577,0.423$ 
A)  $0.291 , - 2.291$ 
B)  $2.291 , - 0.291$ 
C)  $4.582 , - 0.582$ 
D)  $1.577,0.423$

Question 9

Solve. Round results to the nearest thousandth.
-$$2 y ^ { 2 } + 6 y = - 4$$

Accepted Answer

A)  $- 1.000 , - 2.000$ 
B)  $- 2.000 , - 4.000$ 
C)  $2.000,1.000$ 
D)  $0.562 , - 3.562$ 
A)  $- 1.000 , - 2.000$ 
B)  $- 2.000 , - 4.000$ 
C)  $2.000,1.000$ 
D)  $0.562 , - 3.562$

Question 10

Solve.
-$$9 x ^ { 2 } = - 20 x - 3$$

Accepted Answer

A)  $\frac { - 10 \pm \sqrt { 73 } } { 18 }$ 
B)  $\frac { - 10 \pm \sqrt { 127 } } { 9 }$ 
C)  $\frac { - 20 \pm \sqrt { 73 } } { 9 }$ 
D)  $\frac { - 10 \pm \sqrt { 73 } } { 9 }$ 
A)  $\frac { - 10 \pm \sqrt { 73 } } { 18 }$ 
B)  $\frac { - 10 \pm \sqrt { 127 } } { 9 }$ 
C)  $\frac { - 20 \pm \sqrt { 73 } } { 9 }$ 
D)  $\frac { - 10 \pm \sqrt { 73 } } { 9 }$

Question 11

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

Accepted Answer

A)  $\frac { - 3 \pm \sqrt { 7 } } { 4 }$ 
B)  $\frac { - 6 \pm \sqrt { 7 } } { 2 }$ 
C)  $\frac { - 3 \pm \sqrt { 11 } } { 2 }$ 
D)  $\frac { - 3 \pm \sqrt { 7 } } { 2 }$ 
A)  $\frac { - 3 \pm \sqrt { 7 } } { 4 }$ 
B)  $\frac { - 6 \pm \sqrt { 7 } } { 2 }$ 
C)  $\frac { - 3 \pm \sqrt { 11 } } { 2 }$ 
D)  $\frac { - 3 \pm \sqrt { 7 } } { 2 }$

Question 12

Solve the equation by completing the square.
-$30 \mathrm {~d} ^ { 2 } + 61 \mathrm {~d} + 30 = 0$

Accepted Answer

A)  $- \frac { 6 } { 5 } , - \frac { 6 } { 5 }$ 
B)  $\frac { 5 } { 6 } , \frac { 6 } { 5 }$ 
C)  $- \frac { 5 } { 6 } , - \frac { 6 } { 5 }$ 
D)  $\frac { 6 } { 5 } , \frac { 5 } { 6 }$ 
A)  $- \frac { 6 } { 5 } , - \frac { 6 } { 5 }$ 
B)  $\frac { 5 } { 6 } , \frac { 6 } { 5 }$ 
C)  $- \frac { 5 } { 6 } , - \frac { 6 } { 5 }$ 
D)  $\frac { 6 } { 5 } , \frac { 5 } { 6 }$

Question 13

Solve. Give exact solutions.
-$$y ^ { 2 } = 6$$

Accepted Answer

A)  3 
B)  $\pm \sqrt { 6 }$ 
C)  $\sqrt { 6 }$ 
D)  36 
A)  3 
B)  $\pm \sqrt { 6 }$ 
C)  $\sqrt { 6 }$ 
D)  36

Question 14

Solve.
-$$6 x ^ { 2 } = - 16 x - 1$$

Accepted Answer

A)  $\frac { - 8 \pm \sqrt { 70 } } { 6 }$ 
B)  $\frac { - 16 \pm \sqrt { 58 } } { 6 }$ 
C)  $\frac { - 8 \pm \sqrt { 58 } } { 6 }$ 
D)  $\frac { - 8 \pm \sqrt { 58 } } { 12 }$ 
A)  $\frac { - 8 \pm \sqrt { 70 } } { 6 }$ 
B)  $\frac { - 16 \pm \sqrt { 58 } } { 6 }$ 
C)  $\frac { - 8 \pm \sqrt { 58 } } { 6 }$ 
D)  $\frac { - 8 \pm \sqrt { 58 } } { 12 }$

Question 15

Solve the equation by completing the square.
-$$x ^ { 2 } + x + 6 = 0$$

Accepted Answer

A)  $- \frac { 1 } { 2 } \pm \frac { \sqrt { 23 } } { 2 }$ 
B)  $\frac { 1 } { 2 } \pm \frac { \sqrt { 23 } } { 2 }$ 
C)  $\frac { 1 } { 2 } \pm \frac { \sqrt { 23 } } { 2 } \mathrm { i }$ 
D)  $- \frac { 1 } { 2 } \pm \frac { \sqrt { 23 } } { 2 } i$ 
A)  $- \frac { 1 } { 2 } \pm \frac { \sqrt { 23 } } { 2 }$ 
B)  $\frac { 1 } { 2 } \pm \frac { \sqrt { 23 } } { 2 }$ 
C)  $\frac { 1 } { 2 } \pm \frac { \sqrt { 23 } } { 2 } \mathrm { i }$ 
D)  $- \frac { 1 } { 2 } \pm \frac { \sqrt { 23 } } { 2 } i$

Question 16

Solve by completing the square.
-$$z ^ { 2 } + 8 z - 5 = 0$$

Accepted Answer

A)  $- 4 \pm 2 \sqrt { 21 }$ 
B)  $- 1 \pm \sqrt { 21 }$ 
C)  $4 + \sqrt { 21 }$ 
D)  $- 4 \pm \sqrt { 21 }$ 
A)  $- 4 \pm 2 \sqrt { 21 }$ 
B)  $- 1 \pm \sqrt { 21 }$ 
C)  $4 + \sqrt { 21 }$ 
D)  $- 4 \pm \sqrt { 21 }$

Question 17

Solve.
-$$4 x ^ { 2 } = 5 x - 6$$

Accepted Answer

A)  $\frac { 5 } { 8 } \pm \frac { \sqrt { 71 } } { 8 } \mathrm { i }$ 
B)  $\frac { 5 } { 8 } \pm \frac { \sqrt { 71 } } { 8 }$ 
C)  $- \frac { 5 } { 8 } \pm \frac { \sqrt { 71 } } { 8 }$ 
D)  $- \frac { 5 } { 8 } \pm \frac { \sqrt { 71 } } { 8 } i$ 
A)  $\frac { 5 } { 8 } \pm \frac { \sqrt { 71 } } { 8 } \mathrm { i }$ 
B)  $\frac { 5 } { 8 } \pm \frac { \sqrt { 71 } } { 8 }$ 
C)  $- \frac { 5 } { 8 } \pm \frac { \sqrt { 71 } } { 8 }$ 
D)  $- \frac { 5 } { 8 } \pm \frac { \sqrt { 71 } } { 8 } i$

Question 18

Solve.
-A square has an area of 49 square inches. If the same amount is added to the length and removed from the width, the resulting rectangle has an area of 45 square inches. Find the dimensions of the rectangle.

Accepted Answer

A) 4 in. by 9 in. 
B) 3 in. by 4 in. 
C) 5 in. by 10 in. 
D) 5 in. by 9 in. 
A) 4 in. by 9 in. 
B) 3 in. by 4 in. 
C) 5 in. by 10 in. 
D) 5 in. by 9 in.

Question 19

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 $\mathrm { s } = 16 \mathrm { t } ^ { 2 } + 32 \mathrm { t }$, where $s$ is in feet. How long (to the nearest tenth) will it take the ball to fall 280 feet?

Accepted Answer

A)  $3.3 \mathrm { sec }$ 
B)  $10.9 \mathrm { sec }$ 
C)  $3.1 \mathrm { sec }$ 
D)  $4.2 \mathrm { sec }$ 
A)  $3.3 \mathrm { sec }$ 
B)  $10.9 \mathrm { sec }$ 
C)  $3.1 \mathrm { sec }$ 
D)  $4.2 \mathrm { sec }$

Question 20

Solve the problem. Give the answer to the nearest tenth.
-The hang-time function $V ( T ) = 48 \mathrm {~T} ^ { 2 }$, relates vertical leap to hang time. A player has a vertical leap of 30 in. What is his hang time?

Accepted Answer

A)  $0.6 \mathrm { sec }$ 
B)  $37.9 \mathrm { sec }$ 
C)  $1.3 \mathrm { sec }$ 
D)  $0.8 \mathrm { sec }$ 
A)  $0.6 \mathrm { sec }$ 
B)  $37.9 \mathrm { sec }$ 
C)  $1.3 \mathrm { sec }$ 
D)  $0.8 \mathrm { sec }$

Solve. Give exact solutions. - $- 7 \mathrm { k } ^ { 2 } - 11 = - 123$

Find the x-intercepts. - $f ( x ) = 64 x ^ { 2 } - 32 x + 4$

Solve. -Two cars leave an intersection. One car travels north; the other east. When the car traveling north had gone 15 mi, the distance between the cars was 5 mi more than the distance traveled by the car heading east. How far had The eastbound car traveled?

Find the x-intercepts. - $f ( x ) = - x ^ { 2 } + 17 x - 72$

Solve by completing the square. - $\mathrm { y } ^ { 2 } + 4 \mathrm { y } - 3 = 0$

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

Find the x-intercepts. - $f ( x ) = 3 x + x ( x - 5 )$

Solve. Round results to the nearest thousandth. - $3 x ^ { 2 } - 6 x = 2$

Solve. Round results to the nearest thousandth. - $2 y ^ { 2 } + 6 y = - 4$

Solve. - $9 x ^ { 2 } = - 20 x - 3$

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

Solve the equation by completing the square. - $30 \mathrm {~d} ^ { 2 } + 61 \mathrm {~d} + 30 = 0$

Solve. Give exact solutions. - $y ^ { 2 } = 6$

Solve. - $6 x ^ { 2 } = - 16 x - 1$

Solve the equation by completing the square. - $x ^ { 2 } + x + 6 = 0$

Solve by completing the square. - $z ^ { 2 } + 8 z - 5 = 0$

Solve. - $4 x ^ { 2 } = 5 x - 6$

Solve. -A square has an area of 49 square inches. If the same amount is added to the length and removed from the width, the resulting rectangle has an area of 45 square inches. Find the dimensions of the rectangle.

Solve the problem. Give the answer to the nearest tenth. -The hang-time function $V ( T ) = 48 \mathrm {~T} ^ { 2 }$ , relates vertical leap to hang time. A player has a vertical leap of 30 in. What is his hang time?

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

Finding Measures of Central Tendency for Prices and Heights

Filters

Exam 11: Quadratic Equations and Functions

Solve. Give exact solutions. - −7k2−11=−123- 7 \mathrm { k } ^ { 2 } - 11 = - 123−7k2−11=−123

Find the x-intercepts. - f(x)=64x2−32x+4f ( x ) = 64 x ^ { 2 } - 32 x + 4f(x)=64x2−32x+4

Solve. -Two cars leave an intersection. One car travels north; the other east. When the car traveling north had gone 15 mi, the distance between the cars was 5 mi more than the distance traveled by the car heading east. How far had The eastbound car traveled?

Find the x-intercepts. - f(x)=−x2+17x−72f ( x ) = - x ^ { 2 } + 17 x - 72f(x)=−x2+17x−72

Solve by completing the square. - y2+4y−3=0\mathrm { y } ^ { 2 } + 4 \mathrm { y } - 3 = 0y2+4y−3=0

Solve by completing the square. - y2=−3y+9y ^ { 2 } = - 3 y + 9y2=−3y+9

Find the x-intercepts. - f(x)=3x+x(x−5)f ( x ) = 3 x + x ( x - 5 )f(x)=3x+x(x−5)

Solve. Round results to the nearest thousandth. - 3x2−6x=23 x ^ { 2 } - 6 x = 23x2−6x=2

Solve. Round results to the nearest thousandth. - 2y2+6y=−42 y ^ { 2 } + 6 y = - 42y2+6y=−4

Solve. - 9x2=−20x−39 x ^ { 2 } = - 20 x - 39x2=−20x−3

Solve. - 2x2+6x=−12 x ^ { 2 } + 6 x = - 12x2+6x=−1

Solve the equation by completing the square. - 30 d2+61 d+30=030 \mathrm {~d} ^ { 2 } + 61 \mathrm {~d} + 30 = 030 d2+61 d+30=0

Solve. Give exact solutions. - y2=6y ^ { 2 } = 6y2=6

Solve. - 6x2=−16x−16 x ^ { 2 } = - 16 x - 16x2=−16x−1

Solve the equation by completing the square. - x2+x+6=0x ^ { 2 } + x + 6 = 0x2+x+6=0

Solve by completing the square. - z2+8z−5=0z ^ { 2 } + 8 z - 5 = 0z2+8z−5=0

Solve. - 4x2=5x−64 x ^ { 2 } = 5 x - 64x2=5x−6