Question 1

Add the proper constant to each binomial so that the resulting trinomial is a perfect square trinomial. Then factor the
trinomial.
-$x ^ { 2 } - 4 x +$______

Accepted Answer

A)  $x ^ { 2 } - 4 x + ( - 16 ) = ( x - 4 ) ^ { 2 }$ 
B)  $x ^ { 2 } - 4 x + \underline { 4 } = ( x - 2 ) ^ { 2 }$ 
C)  $x ^ { 2 } - 4 x + ( - 4 ) = ( x - 2 ) ^ { 2 }$ 
D)  $x ^ { 2 } - 4 x + \underline { 16 } = ( x - 4 ) ^ { 2 }$ 
A)  $x ^ { 2 } - 4 x + ( - 16 ) = ( x - 4 ) ^ { 2 }$ 
B)  $x ^ { 2 } - 4 x + \underline { 4 } = ( x - 2 ) ^ { 2 }$ 
C)  $x ^ { 2 } - 4 x + ( - 4 ) = ( x - 2 ) ^ { 2 }$ 
D)  $x ^ { 2 } - 4 x + \underline { 16 } = ( x - 4 ) ^ { 2 }$

Question 2

Solve the equation by completing the square.
-$16 \mathrm { x } ^ { 2 } + 1 = 7 \mathrm { x }$

Accepted Answer

A)  $\frac { - 7 - i \sqrt { 15 } } { 32 } , \frac { - 7 + i \sqrt { 15 } } { 32 }$ 
B)  $\frac { 7 - i \sqrt { 15 } } { 32 } , \frac { 7 + i \sqrt { 15 } } { 32 }$ 
C)  $\frac { - 7 - \mathrm { i } \sqrt { 15 } } { 32 } , \frac { 7 + \mathrm { i } \sqrt { 15 } } { 32 }$ 
D)  $\frac { 7 - \mathrm { i } \sqrt { 15 } } { 32 } , \frac { - 7 + \mathrm { i } \sqrt { 15 } } { 32 }$ 
A)  $\frac { - 7 - i \sqrt { 15 } } { 32 } , \frac { - 7 + i \sqrt { 15 } } { 32 }$ 
B)  $\frac { 7 - i \sqrt { 15 } } { 32 } , \frac { 7 + i \sqrt { 15 } } { 32 }$ 
C)  $\frac { - 7 - \mathrm { i } \sqrt { 15 } } { 32 } , \frac { 7 + \mathrm { i } \sqrt { 15 } } { 32 }$ 
D)  $\frac { 7 - \mathrm { i } \sqrt { 15 } } { 32 } , \frac { - 7 + \mathrm { i } \sqrt { 15 } } { 32 }$

Question 3

Solve the inequality. Graph the solution set and write the solution set in interval notation.
-$\frac { x - 3 } { x + 1 } < 0$

Accepted Answer

A)  $( - \infty , - 1 ) \cup ( 3 , \infty )$
  
B)  $( 3 , \infty )$
  
C)  $( - 1,3 )$
  
D)  $( - \infty , - 1 )$
  
A)  $( - \infty , - 1 ) \cup ( 3 , \infty )$
  
B)  $( 3 , \infty )$
  
C)  $( - 1,3 )$
  
D)  $( - \infty , - 1 )$

Question 4

Solve.
-A rectangular sign must have an area of 23 square yards. Its length must be 2 yards more than its width. Find the dimensions of the sign.

Accepted Answer

A)  $( 1 + 2 \sqrt { 6 } )$ yd by $( - 1 + 2 \sqrt { 6 } ) y d$ 
B)  $( 1 - 2 \sqrt { 6 } )$ yd by $( - 1 - 2 \sqrt { 6 } ) y d$ 
C)  $( 1 - 2 \sqrt { 6 } ) \mathrm { yd }$ by $( 1 + 2 \sqrt { 6 } ) \mathrm { yd }$ 
D)  $( 1 + 2 \sqrt { 6 } )$ yd by $( 3 + 2 \sqrt { 6 } ) y d$ 
A)  $( 1 + 2 \sqrt { 6 } )$ yd by $( - 1 + 2 \sqrt { 6 } ) y d$ 
B)  $( 1 - 2 \sqrt { 6 } )$ yd by $( - 1 - 2 \sqrt { 6 } ) y d$ 
C)  $( 1 - 2 \sqrt { 6 } ) \mathrm { yd }$ by $( 1 + 2 \sqrt { 6 } ) \mathrm { yd }$ 
D)  $( 1 + 2 \sqrt { 6 } )$ yd by $( 3 + 2 \sqrt { 6 } ) y d$

Question 5

Find the maximum or minimum value of the function. Approximate to two decimal places.
-$f ( x ) = - 8.4 x ^ { 2 } - 1.9 x - 9.3$

Accepted Answer

A)  $2.03$ 
B)  $- 9.19$ 
C)  $- 9.62$ 
D)  $- 0.11$ 
A)  $2.03$ 
B)  $- 9.19$ 
C)  $- 9.62$ 
D)  $- 0.11$

Question 6

Given the accompanying graph of y = f(x), sketch the graph of the following.
-$y = f ( x - 2 ) + 5$
 
$y = f ( x )$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 7

Solve the equation by completing the square.
-$x ^ { 2 } + 18 x + 58 = 0$

Accepted Answer

A)  $- 18 + \sqrt { 58 }$ 
B)  $9 + \sqrt { 23 }$ 
C)  $- 9 - \sqrt { 23 } , - 9 + \sqrt { 23 }$ 
D)  $9 - \sqrt { 58 } , 9 + \sqrt { 58 }$ 
A)  $- 18 + \sqrt { 58 }$ 
B)  $9 + \sqrt { 23 }$ 
C)  $- 9 - \sqrt { 23 } , - 9 + \sqrt { 23 }$ 
D)  $9 - \sqrt { 58 } , 9 + \sqrt { 58 }$

Question 8

Use the discriminant to determine the number and type of solutions of the equation.
-$x ^ { 2 } - 3 x - 5 = 0$

Accepted Answer

A)  two complex but not real solutions 
B)  two real solutions 
C)  one real solution 
A)  two complex but not real solutions 
B)  two real solutions 
C)  one real solution

Question 9

Solve.
-$x ^ { 4 } - 5 x ^ { 2 } - 36 = 0$

Accepted Answer

A)  $- 9,9 , - 4 i , 4 i$ 
B)  $- 3,3 , - 2 \mathrm { i } , 2 \mathrm { i }$ 
C)  $- 2,2 , - 3 i , 3 i$ 
D)  $- 3,3 , - 2,2$ 
A)  $- 9,9 , - 4 i , 4 i$ 
B)  $- 3,3 , - 2 \mathrm { i } , 2 \mathrm { i }$ 
C)  $- 2,2 , - 3 i , 3 i$ 
D)  $- 3,3 , - 2,2$

Question 10

Solve the inequality. Graph the solution set and write the solution set in interval notation.
-$x ^ { 2 } + 13 x + 42 > 0$

Accepted Answer

A)  $( - \infty , - 7 )$
  
B)  $( - 6 , \infty )$
  
C)  $( - \infty , - 7 ) \cup ( - 6 , \infty )$
  
D)  $( - 7 , - 6 )$
  
A)  $( - \infty , - 7 )$
  
B)  $( - 6 , \infty )$
  
C)  $( - \infty , - 7 ) \cup ( - 6 , \infty )$
  
D)  $( - 7 , - 6 )$

Question 11

Solve the inequality. Graph the solution set and write the solution set in interval notation.
-$\mathrm { x } ^ { 2 } - 5 \mathrm { x } - 6 < 0$

Accepted Answer

A)  $( 6 , \infty )$
  
B)  $( - 1,6 )$
  
C)  $( - \infty , - 1 )$
  
D)  $( - \infty , - 1 ) \cup ( 6 , \infty )$
  
A)  $( 6 , \infty )$
  
B)  $( - 1,6 )$
  
C)  $( - \infty , - 1 )$
  
D)  $( - \infty , - 1 ) \cup ( 6 , \infty )$

Question 12

Solve.
-A ball is thrown upward with an initial velocity of 21 meters per second from a cliff that is 70 meters high. The height of the ball is given by the quadratic equation $h = - 4.9 t ^ { 2 } + 21 t + 110$ where $\mathrm { h }$ is in meters and $\mathrm { t }$ is the time in seconds since the ball was thrown. Find the time that the ball will be 40 meters from the ground. Round your answer to the nearest tenth of a second.

Accepted Answer

A)  $7.3 \mathrm { sec }$ 
B)  $7.4 \mathrm { sec }$ 
C)  $6.6 \mathrm { sec }$ 
D)  $6.5 \mathrm { sec }$ 
A)  $7.3 \mathrm { sec }$ 
B)  $7.4 \mathrm { sec }$ 
C)  $6.6 \mathrm { sec }$ 
D)  $6.5 \mathrm { sec }$

Question 13

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

Accepted Answer

A)  $- 3,2$ 
B)  $- \frac { 1 } { 3 } , \frac { 1 } { 2 }$ 
C)  $3 , - 2$ 
D)  $\frac { 1 } { 3 } , - \frac { 1 } { 2 }$ 
A)  $- 3,2$ 
B)  $- \frac { 1 } { 3 } , \frac { 1 } { 2 }$ 
C)  $3 , - 2$ 
D)  $\frac { 1 } { 3 } , - \frac { 1 } { 2 }$

Question 14

Find two possible missing terms so that the expression is a perfect square trinomial.
-$\mathrm { x } ^ { 2 } + \ldots + \frac { 1 } { 4 }$

Accepted Answer

A)  $- \frac { 1 } { 2 } , \frac { 1 } { 2 }$ 
B)  $- 2 x , 2 x$ 
C)  $- x , x$ 
D)  $- \frac { 1 } { 2 } x , \frac { 1 } { 2 } x$ 
A)  $- \frac { 1 } { 2 } , \frac { 1 } { 2 }$ 
B)  $- 2 x , 2 x$ 
C)  $- x , x$ 
D)  $- \frac { 1 } { 2 } x , \frac { 1 } { 2 } x$

Question 15

Use the quadratic formula and a calculator to approximate the solution to the nearest tenth.
-$3 x ^ { 2 } + 2 x - 2 = 0$

Accepted Answer

A)  $0.5 , - 1.2$ 
B)  $1.2 , - 0.5$ 
C)  $1.1 , - 2.4$ 
D)  $4.3 , - 5$ 
A)  $0.5 , - 1.2$ 
B)  $1.2 , - 0.5$ 
C)  $1.1 , - 2.4$ 
D)  $4.3 , - 5$

Question 16

Sketch the graph of the quadratic function. Give the vertex and axis of symmetry.
-$f ( x ) = - \frac { 1 } { 4 } ( x + 5 ) ^ { 2 } - 4$

Accepted Answer

A)  vertex $( 4,5 )$; axis $x = 4$
  
B)  vertex $( - 5 , - 4 )$; axis $x = - 5$
  
C)  vertex $( - 4 , - 5 )$; axis $x = - 4$
  
D)  vertex $( 5 , - 4 )$; axis $x = 5$
  
A)  vertex $( 4,5 )$; axis $x = 4$
  
B)  vertex $( - 5 , - 4 )$; axis $x = - 5$
  
C)  vertex $( - 4 , - 5 )$; axis $x = - 4$
  
D)  vertex $( 5 , - 4 )$; axis $x = 5$

Question 17

Solve the inequality. Graph the solution set and write the solution set in interval notation.
-$( x + 6 ) ( x - 5 ) > 0$

Accepted Answer

A)  $( - \infty , - 6 ] \cup [ 5 , \infty )$
  
B)  $( - \infty , - 6 ) \cup ( 5 , \infty )$
  
C)  $[ - 6,5 ]$
  
D)  $( - 6,5 )$
  
A)  $( - \infty , - 6 ] \cup [ 5 , \infty )$
  
B)  $( - \infty , - 6 ) \cup ( 5 , \infty )$
  
C)  $[ - 6,5 ]$
  
D)  $( - 6,5 )$

Question 18

Solve the inequality. Graph the solution set and write the solution set in interval notation.
-$\frac { ( x - 4 ) ( x + 4 ) } { x } \leq 0$

Accepted Answer

A) $(-\infty,-4] \cup(0,4]$
  
B)  $[ - 4,0 ) \cup [ 4 , \infty )$
  
C) $[ - 4,0 ) \cup ( 0,4 ]$
  
D)  $( - \infty , - 4 ] \cup [ 4 , \infty )$
  
A) $(-\infty,-4] \cup(0,4]$
  
B)  $[ - 4,0 ) \cup [ 4 , \infty )$
  
C) $[ - 4,0 ) \cup ( 0,4 ]$
  
D)  $( - \infty , - 4 ] \cup [ 4 , \infty )$

Question 19

Solve the inequality. Write the solution set in interval notation.
-$\frac { 4 } { x - 2 } < 1$

Accepted Answer

A)  $( - \infty , 2 ] \cup [ 6 , \infty )$ 
B)  $( - \infty , 2 ) \cup ( 6 , \infty )$ 
C)  $( - \infty , 2 )$ 
D)  $( 2,6 )$ 
A)  $( - \infty , 2 ] \cup [ 6 , \infty )$ 
B)  $( - \infty , 2 ) \cup ( 6 , \infty )$ 
C)  $( - \infty , 2 )$ 
D)  $( 2,6 )$

Question 20

Solve the inequality. Graph the solution set and write the solution set in interval notation.
-$\frac { x } { x + 1 } > 0$

Accepted Answer

A) $(-\infty,-1) \cup(0, \infty)$
  
B)  $( - \infty , - 1 ] \cup [ 0 , \infty )$
  
C) $( 0 , \infty )$
  
D)  $( - 1,0 ]$
  
A) $(-\infty,-1) \cup(0, \infty)$
  
B)  $( - \infty , - 1 ] \cup [ 0 , \infty )$
  
C) $( 0 , \infty )$
  
D)  $( - 1,0 ]$

Add the proper constant to each binomial so that the resulting trinomial is a perfect square trinomial. Then factor the trinomial. - $x ^ { 2 } - 4 x +$ ______

Solve the equation by completing the square. - $16 \mathrm { x } ^ { 2 } + 1 = 7 \mathrm { x }$

Solve the inequality. Graph the solution set and write the solution set in interval notation. - $\frac { x - 3 } { x + 1 } < 0$ $Solve the inequality. Graph the solution set and write the solution set in interval notation. - \frac { x - 3 } { x + 1 } < 0$

Solve. -A rectangular sign must have an area of 23 square yards. Its length must be 2 yards more than its width. Find the dimensions of the sign.

Find the maximum or minimum value of the function. Approximate to two decimal places. - $f ( x ) = - 8.4 x ^ { 2 } - 1.9 x - 9.3$

Given the accompanying graph of y = f(x), sketch the graph of the following. - $y = f ( x - 2 ) + 5$ $y = f ( x )$

Solve the equation by completing the square. - $x ^ { 2 } + 18 x + 58 = 0$

Use the discriminant to determine the number and type of solutions of the equation. - $x ^ { 2 } - 3 x - 5 = 0$

Solve. - $x ^ { 4 } - 5 x ^ { 2 } - 36 = 0$

Solve the inequality. Graph the solution set and write the solution set in interval notation. - $x ^ { 2 } + 13 x + 42 > 0$ $Solve the inequality. Graph the solution set and write the solution set in interval notation. - x ^ { 2 } + 13 x + 42 > 0$

Solve the inequality. Graph the solution set and write the solution set in interval notation. - $\mathrm { x } ^ { 2 } - 5 \mathrm { x } - 6 < 0$ $Solve the inequality. Graph the solution set and write the solution set in interval notation. - \mathrm { x } ^ { 2 } - 5 \mathrm { x } - 6 < 0$

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

Find two possible missing terms so that the expression is a perfect square trinomial. - $\mathrm { x } ^ { 2 } + \ldots + \frac { 1 } { 4 }$

Use the quadratic formula and a calculator to approximate the solution to the nearest tenth. - $3 x ^ { 2 } + 2 x - 2 = 0$

Sketch the graph of the quadratic function. Give the vertex and axis of symmetry. - $f ( x ) = - \frac { 1 } { 4 } ( x + 5 ) ^ { 2 } - 4$ $Sketch the graph of the quadratic function. Give the vertex and axis of symmetry. - f ( x ) = - \frac { 1 } { 4 } ( x + 5 ) ^ { 2 } - 4$

Solve the inequality. Graph the solution set and write the solution set in interval notation. - $( x + 6 ) ( x - 5 ) > 0$

Solve the inequality. Graph the solution set and write the solution set in interval notation. - $\frac { ( x - 4 ) ( x + 4 ) } { x } \leq 0$ $Solve the inequality. Graph the solution set and write the solution set in interval notation. - \frac { ( x - 4 ) ( x + 4 ) } { x } \leq 0$

Solve the inequality. Write the solution set in interval notation. - $\frac { 4 } { x - 2 } < 1$

Solve the inequality. Graph the solution set and write the solution set in interval notation. - $\frac { x } { x + 1 } > 0$ $Solve the inequality. Graph the solution set and write the solution set in interval notation. - \frac { x } { x + 1 } > 0$

Review of Real Numbers

Equations, Inequalities, and Problem Solving

Graphing

Solving Systems of Linear Equations

Exponents and Polynomials

Factoring Polynomials

Rational Expressions

More on Functions and Graphs

Inequalities and Absolute Value

Rational Exponents, Radicals, and Complex Numbers

Exponential and Logarithmic Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Exam 11: Quadratic Equations and Functions

Add the proper constant to each binomial so that the resulting trinomial is a perfect square trinomial. Then factor the trinomial. - x2−4x+x ^ { 2 } - 4 x +x2−4x+ ______

Solve the equation by completing the square. - 16x2+1=7x16 \mathrm { x } ^ { 2 } + 1 = 7 \mathrm { x }16x2+1=7x

Solve the inequality. Graph the solution set and write the solution set in interval notation. - x−3x+1<0\frac { x - 3 } { x + 1 } < 0x+1x−3​<0

Solve. -A rectangular sign must have an area of 23 square yards. Its length must be 2 yards more than its width. Find the dimensions of the sign.

Find the maximum or minimum value of the function. Approximate to two decimal places. - f(x)=−8.4x2−1.9x−9.3f ( x ) = - 8.4 x ^ { 2 } - 1.9 x - 9.3f(x)=−8.4x2−1.9x−9.3

Given the accompanying graph of y = f(x), sketch the graph of the following. - y=f(x−2)+5y = f ( x - 2 ) + 5y=f(x−2)+5 y=f(x)y = f ( x )y=f(x)

Solve the equation by completing the square. - x2+18x+58=0x ^ { 2 } + 18 x + 58 = 0x2+18x+58=0

Use the discriminant to determine the number and type of solutions of the equation. - x2−3x−5=0x ^ { 2 } - 3 x - 5 = 0x2−3x−5=0

Solve. - x4−5x2−36=0x ^ { 4 } - 5 x ^ { 2 } - 36 = 0x4−5x2−36=0

Solve the inequality. Graph the solution set and write the solution set in interval notation. - x2+13x+42>0x ^ { 2 } + 13 x + 42 > 0x2+13x+42>0

Solve the inequality. Graph the solution set and write the solution set in interval notation. - x2−5x−6<0\mathrm { x } ^ { 2 } - 5 \mathrm { x } - 6 < 0x2−5x−6<0

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

Find two possible missing terms so that the expression is a perfect square trinomial. - x2+…+14\mathrm { x } ^ { 2 } + \ldots + \frac { 1 } { 4 }x2+…+41​

Use the quadratic formula and a calculator to approximate the solution to the nearest tenth. - 3x2+2x−2=03 x ^ { 2 } + 2 x - 2 = 03x2+2x−2=0

Sketch the graph of the quadratic function. Give the vertex and axis of symmetry. - f(x)=−14(x+5)2−4f ( x ) = - \frac { 1 } { 4 } ( x + 5 ) ^ { 2 } - 4f(x)=−41​(x+5)2−4

Solve the inequality. Graph the solution set and write the solution set in interval notation. - (x+6)(x−5)>0( x + 6 ) ( x - 5 ) > 0(x+6)(x−5)>0

Solve the inequality. Graph the solution set and write the solution set in interval notation. - (x−4)(x+4)x≤0\frac { ( x - 4 ) ( x + 4 ) } { x } \leq 0x(x−4)(x+4)​≤0

Solve the inequality. Write the solution set in interval notation. - 4x−2<1\frac { 4 } { x - 2 } < 1x−24​<1

Solve the inequality. Graph the solution set and write the solution set in interval notation. - xx+1>0\frac { x } { x + 1 } > 0x+1x​>0