Question 1

Find the axis of symmetry associated with the quadratic equation.
-$$y = x ^ { 2 } - 8 x + 16$$

Accepted Answer

A)  $x = - 4$ 
B)  $x = 9$ 
C)  $x = 4$ 
D)  $x = - 9$ 
A)  $x = - 4$ 
B)  $x = 9$ 
C)  $x = 4$ 
D)  $x = - 9$ C

Question 2

Solve the problem.
-A rectangular space of 252 square feet is allocated for the living and dining areas in an apartment. Find the width of the square living area given that the width of the dining area is 9 ft.  
$$\text { Total Area: } 252 \text { sq. ft }$$

Accepted Answer

A)  21 ft 
B)  12 ft 
C)  14 ft 
D)  11 ft 
A)  21 ft 
B)  12 ft 
C)  14 ft 
D)  11 ft B

Question 3

Solve by extracting square roots.
-$x ^ { 2 } - 10 x$

Accepted Answer

A)  $25 ; ( x - 5 ) ^ { 2 }$ 
B)  $0 ; ( x - 5 ) ^ { 2 }$ 
C)  $25 ; ( x + 5 ) ^ { 2 }$ 
D)  $25 ; ( x - 10 ) ^ { 2 }$ 
A)  $25 ; ( x - 5 ) ^ { 2 }$ 
B)  $0 ; ( x - 5 ) ^ { 2 }$ 
C)  $25 ; ( x + 5 ) ^ { 2 }$ 
D)  $25 ; ( x - 10 ) ^ { 2 }$ A

Question 4

Solve the problem.
-Working together, Rick and Juanita can complete a job in 6 hours. It would take Rick 9 hours longer than Juanita to do the job alone. How long would it take Juanita alone?

Accepted Answer

A)  6 hr 
B)  3 hr 
C)  15 hr 
D)  9 hr 
A)  6 hr 
B)  3 hr 
C)  15 hr 
D)  9 hr

Question 5

Solve the problem.
-Given $f ( x ) = \frac { x - 3 } { x + 2 }$, find all values for $x$ for which $f ( x ) > 0$.

Accepted Answer

A)  $( - 2,3 )$ 
B)  $( 3 , \infty )$ 
C)  $( - \infty , - 2 ) \cup ( 3 , \infty )$ 
D)  $( - \infty , - 2 )$ 
A)  $( - 2,3 )$ 
B)  $( 3 , \infty )$ 
C)  $( - \infty , - 2 ) \cup ( 3 , \infty )$ 
D)  $( - \infty , - 2 )$

Question 6

Solve the problem.
-On a sunny day, a tree and its shadow form the sides of a right triangle. If the hypotenuse is 52 m long and the tree is 48 m tall, how long is the shadow?

Accepted Answer

A)  32 m 
B) 71 m 
C) 20m 
D)  100 m 
A)  32 m 
B) 71 m 
C) 20m 
D)  100 m

Question 7

Solve the problem. Approximate to the nearest tenth when necessary.
-The area of a circle is 53 square feet. Find the radius of the circle.

Accepted Answer

A)  16.9 ft 
B)  4.1 ft 
C)  12.9 ft 
D)  7.3 ft 
A)  16.9 ft 
B)  4.1 ft 
C)  12.9 ft 
D)  7.3 ft

Question 8

Find the vertex of the parabola associated with the quadratic equation.
-$$y = 4 x ^ { 2 } + 16 x + 19$$

Accepted Answer

A)  $( - 3,2 )$ 
B)  $( - 2,3 )$ 
C)  $( 3 , - 2 )$ 
D)  $( 2 , - 3 )$ 
A)  $( - 3,2 )$ 
B)  $( - 2,3 )$ 
C)  $( 3 , - 2 )$ 
D)  $( 2 , - 3 )$

Question 9

Solve the equation by completing the square.
-$$x ^ { 2 } + 4 x + 13 = 0$$

Accepted Answer

A)  $\{ - 2 \pm \sqrt { 13 } i \}$ 
B)  $\{ - 2 \pm 3 i \}$ 
C)  $\{ 2 \pm 3 \mathrm { i } \}$ 
D)  $\{ 1 , - 5 \}$ 
A)  $\{ - 2 \pm \sqrt { 13 } i \}$ 
B)  $\{ - 2 \pm 3 i \}$ 
C)  $\{ 2 \pm 3 \mathrm { i } \}$ 
D)  $\{ 1 , - 5 \}$

Question 10

Find the vertex of the parabola associated with the quadratic equation.
-$$y = x ^ { 2 } - 12 x + 45$$

Accepted Answer

A)  $( 9,6 )$ 
B)  $( 0,6 )$ 
C)  $( 6,9 )$ 
D)  $( 9,0 )$ 
A)  $( 9,6 )$ 
B)  $( 0,6 )$ 
C)  $( 6,9 )$ 
D)  $( 9,0 )$

Question 11

Find the x- and y-intercepts of the parabola associated with the quadratic equation. If the parabola does not have any
x-intercepts, state ʺno x-intercepts.ʺ
-$$y = - x ^ { 2 } - 6 x - 10$$

Accepted Answer

A)  $\left\{ \frac { 6 \pm \sqrt { 76 } } { 2 } , 0 \right) , ( 0 , - 10 )$ 
B)  No $x$-intercepts, $( 0 , - 10 )$ 
C)  $\left\{ \frac { 6 \pm \sqrt { 76 } } { 2 } , 0 \right\} , ( 0,10 )$ 
D)  No x-intercepts, $( 0,10 )$ 
A)  $\left\{ \frac { 6 \pm \sqrt { 76 } } { 2 } , 0 \right) , ( 0 , - 10 )$ 
B)  No $x$-intercepts, $( 0 , - 10 )$ 
C)  $\left\{ \frac { 6 \pm \sqrt { 76 } } { 2 } , 0 \right\} , ( 0,10 )$ 
D)  No x-intercepts, $( 0,10 )$

Question 12

Solve the problem. Approximate to the nearest tenth when necessary.
-The area of a circle is 36π square meters. Find the radius of the circle.

Accepted Answer

A)  6 m 
B) 36 m 
C)  10.6 m 
D)  18.8 m 
A)  6 m 
B) 36 m 
C)  10.6 m 
D)  18.8 m

Question 13

Find the x- and y-intercepts of the parabola associated with the quadratic equation. If the parabola does not have any
x-intercepts, state ʺno x-intercepts.ʺ
-$$y = - x ^ { 2 } + 17 x - 72$$

Accepted Answer

A)  No x-intercepts, $( 0,8 )$ 
B)  $( 8,0 ) , ( 9,0 ) , ( 0 , - 72 )$ 
C)  $( 8,0 ) , ( 9,0 ) , ( 0,8 )$ 
D)  $( - 8,0 ) , ( - 9,0 ) , ( 0 , - 72 )$ 
A)  No x-intercepts, $( 0,8 )$ 
B)  $( 8,0 ) , ( 9,0 ) , ( 0 , - 72 )$ 
C)  $( 8,0 ) , ( 9,0 ) , ( 0,8 )$ 
D)  $( - 8,0 ) , ( - 9,0 ) , ( 0 , - 72 )$

Question 14

Find the x- and y-intercepts of the parabola associated with the quadratic equation. If the parabola does not have any
x-intercepts, state ʺno x-intercepts.ʺ
-$$y = x ^ { 2 } - 6 x + 9$$

Accepted Answer

A)  $( - 3,0 ) , ( 0,9 )$ 
B)  $( 9,0 ) , ( 0 , - 3 )$ 
C)  $( 9,0 ) , ( 0,3 )$ 
D)  $( 3,0 ) , ( 0,9 )$ 
A)  $( - 3,0 ) , ( 0,9 )$ 
B)  $( 9,0 ) , ( 0 , - 3 )$ 
C)  $( 9,0 ) , ( 0,3 )$ 
D)  $( 3,0 ) , ( 0,9 )$

Question 15

Solve by extracting square roots.
-$$x ^ { 2 } - 25 = 0$$

Accepted Answer

A)  $\{ 5 , - 5 \}$ 
B)  $\{ 14 \}$ 
C)  $\{ 4 , - 4 \}$ 
D)  $\{ 5 \}$ 
A)  $\{ 5 , - 5 \}$ 
B)  $\{ 14 \}$ 
C)  $\{ 4 , - 4 \}$ 
D)  $\{ 5 \}$

Question 16

Solve the problem.
-The two legs of a right triangle are 10 meters and 20 meters, respectively. Find the hypotenuse of the triangle, rounded to the nearest hundredth of a meter.

Accepted Answer

A)  250 m 
B)  22.36 m 
C) 15m 
D)  500 m 
A)  250 m 
B)  22.36 m 
C) 15m 
D)  500 m

Question 17

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

Accepted Answer

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

Question 18

Find the axis of symmetry associated with the quadratic equation.
-$$y = - 3 x ^ { 2 } + 12 x - 9$$

Accepted Answer

A)  $x = 2$ 
B)  $x = - 3$ 
C)  $x = - 2$ 
D)  $x = 3$ 
A)  $x = 2$ 
B)  $x = - 3$ 
C)  $x = - 2$ 
D)  $x = 3$

Question 19

Solve by extracting square roots.
-$x ^ { 2 } - 12 x$

Accepted Answer

A)  $0 ; ( x - 6 ) ^ { 2 }$ 
B)  $36 ; ( x + 6 ) ^ { 2 }$ 
C)  $36 ; ( x - 6 ) ^ { 2 }$ 
D)  $36 ; ( x - 12 )$ 
A)  $0 ; ( x - 6 ) ^ { 2 }$ 
B)  $36 ; ( x + 6 ) ^ { 2 }$ 
C)  $36 ; ( x - 6 ) ^ { 2 }$ 
D)  $36 ; ( x - 12 )$

Question 20

Solve the equation by completing the square.
-$$x ^ { 2 } + 5 x = 24$$

Accepted Answer

A)  $\{ - 8,3 \}$ 
B)  $\{ 8,3 \}$ 
C)  $\{ - 8 , - 3 \}$ 
D)  $\{ - 3,8 \}$ 
A)  $\{ - 8,3 \}$ 
B)  $\{ 8,3 \}$ 
C)  $\{ - 8 , - 3 \}$ 
D)  $\{ - 3,8 \}$

Find the axis of symmetry associated with the quadratic equation. - $y = x ^ { 2 } - 8 x + 16$

Solve by extracting square roots. - $x ^ { 2 } - 10 x$

Solve the problem. -Working together, Rick and Juanita can complete a job in 6 hours. It would take Rick 9 hours longer than Juanita to do the job alone. How long would it take Juanita alone?

Solve the problem. -Given $f ( x ) = \frac { x - 3 } { x + 2 }$ , find all values for $x$ for which $f ( x ) > 0$ .

Solve the problem. -On a sunny day, a tree and its shadow form the sides of a right triangle. If the hypotenuse is 52 m long and the tree is 48 m tall, how long is the shadow?

Solve the problem. Approximate to the nearest tenth when necessary. -The area of a circle is 53 square feet. Find the radius of the circle.

Find the vertex of the parabola associated with the quadratic equation. - $y = 4 x ^ { 2 } + 16 x + 19$

Solve the equation by completing the square. - $x ^ { 2 } + 4 x + 13 = 0$

Find the vertex of the parabola associated with the quadratic equation. - $y = x ^ { 2 } - 12 x + 45$

Find the x- and y-intercepts of the parabola associated with the quadratic equation. If the parabola does not have any x-intercepts, state ʺno x-intercepts.ʺ - $y = - x ^ { 2 } - 6 x - 10$

Solve the problem. Approximate to the nearest tenth when necessary. -The area of a circle is 36π square meters. Find the radius of the circle.

Find the x- and y-intercepts of the parabola associated with the quadratic equation. If the parabola does not have any x-intercepts, state ʺno x-intercepts.ʺ - $y = - x ^ { 2 } + 17 x - 72$

Find the x- and y-intercepts of the parabola associated with the quadratic equation. If the parabola does not have any x-intercepts, state ʺno x-intercepts.ʺ - $y = x ^ { 2 } - 6 x + 9$

Solve by extracting square roots. - $x ^ { 2 } - 25 = 0$

Solve the problem. -The two legs of a right triangle are 10 meters and 20 meters, respectively. Find the hypotenuse of the triangle, rounded to the nearest hundredth of a meter.

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

Find the axis of symmetry associated with the quadratic equation. - $y = - 3 x ^ { 2 } + 12 x - 9$

Solve by extracting square roots. - $x ^ { 2 } - 12 x$

Solve the equation by completing the square. - $x ^ { 2 } + 5 x = 24$

Review of Real Numbers

Linear Equations

Graphing Linear Equations

Systems of Equations

Exponents and Polynomials

Factoring and Quadratic Equations

Rational Expressions and Equations

A Transition

Radical Expressions and Equations

Functions

Logarithmic and Exponential Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Exam 10: Quadratic Equations

Find the axis of symmetry associated with the quadratic equation. - y=x2−8x+16y = x ^ { 2 } - 8 x + 16y=x2−8x+16

Solve the problem. -A rectangular space of 252 square feet is allocated for the living and dining areas in an apartment. Find the width of the square living area given that the width of the dining area is 9 ft. Total Area: 252 sq. ft \text { Total Area: } 252 \text { sq. ft } Total Area: 252 sq. ft

Solve by extracting square roots. - x2−10xx ^ { 2 } - 10 xx2−10x