Question 1

Use the quadratic formula to solve the equation.
-$$\frac { 1 } { 10 } x ^ { 2 } + x + 1 = 0$$

Accepted Answer

A)  $\{ - 10 + \sqrt { 10 } \}$ 
B)  $\{ 5 - \sqrt { 10 } , 5 + \sqrt { 10 } \}$ 
C)  $\{ 5 + \sqrt { 15 } \}$ 
D)  $\{ - 5 - \sqrt { 15 } , - 5 + \sqrt { 15 } \}$ 
A)  $\{ - 10 + \sqrt { 10 } \}$ 
B)  $\{ 5 - \sqrt { 10 } , 5 + \sqrt { 10 } \}$ 
C)  $\{ 5 + \sqrt { 15 } \}$ 
D)  $\{ - 5 - \sqrt { 15 } , - 5 + \sqrt { 15 } \}$

Question 2

Use the square root property to solve the equation.
$( x + 2 ) ^ { 2 } = 17$

Accepted Answer

A)  $\{ 15 \}$ 
B)  $\{ 2 - \sqrt { 17 } , 2 + \sqrt { 17 } \}$ 
C)  $\{ - 2 - \sqrt { 17 } , - 2 + \sqrt { 17 } \}$ 
D)  $\{ - \sqrt { 17 } , \sqrt { 17 } \}$ 
A)  $\{ 15 \}$ 
B)  $\{ 2 - \sqrt { 17 } , 2 + \sqrt { 17 } \}$ 
C)  $\{ - 2 - \sqrt { 17 } , - 2 + \sqrt { 17 } \}$ 
D)  $\{ - \sqrt { 17 } , \sqrt { 17 } \}$

Question 3

Solve the inequality. Write the solution set in interval notation.
-$$( x + 7 ) ( x - 1 ) ( x - 4 ) < 0$$

Accepted Answer

A)  $( - \infty , - 7 ) \cup ( 1,4 )$ 
B)  $( - 7,1 ) \cup ( 4 , \infty )$ 
C)  $( - \infty , 1 )$ 
D)  $( 4 , \infty )$ 
A)  $( - \infty , - 7 ) \cup ( 1,4 )$ 
B)  $( - 7,1 ) \cup ( 4 , \infty )$ 
C)  $( - \infty , 1 )$ 
D)  $( 4 , \infty )$

Question 4

Find the vertex of the graph of the quadratic function. Find any intercepts and graph the function.
-$f ( x ) = 2 x ^ { 2 } + 8 x$

Accepted Answer

A)  Vertex: $( 0,8 )$;
x-intercepts: none;
y-intercept: $( 0,8 )$
  
B)  Vertex: $( - 2 , - 8 )$;
$x$-intercepts: $( 0,0 )$ and $( 4,0 )$;
$\mathrm { y }$-intercept: $( 0,0 )$
  
C)  Vertex: $( 0 , - 8 )$;
$x$-intercepts: $( - 2,0 )$ and $( 2,0 )$;
$y$-intercept: $( 0 , - 8 )$
  
D)  Vertex: $( 2 , - 8 )$;
$x$-intercepts: $( 0,0 )$ and $( 4,0 )$;
$y$-intercept: $( 0,0 )$
  
A)  Vertex: $( 0,8 )$;
x-intercepts: none;
y-intercept: $( 0,8 )$
  
B)  Vertex: $( - 2 , - 8 )$;
$x$-intercepts: $( 0,0 )$ and $( 4,0 )$;
$\mathrm { y }$-intercept: $( 0,0 )$
  
C)  Vertex: $( 0 , - 8 )$;
$x$-intercepts: $( - 2,0 )$ and $( 2,0 )$;
$y$-intercept: $( 0 , - 8 )$
  
D)  Vertex: $( 2 , - 8 )$;
$x$-intercepts: $( 0,0 )$ and $( 4,0 )$;
$y$-intercept: $( 0,0 )$

Question 5

Solve the inequality. Write the solution set in interval notation.
-$$( 3 x - 4 ) ( x + 2 ) \leq 0$$

Accepted Answer

A)  $( - \infty , - 2 ] \cup \left[ \frac { 4 } { 3 } , \infty \right]$ 
B)  $[ - 2 , \infty )$ 
C)  $\left[ - \infty , \frac { 4 } { 3 } \right]$ 
D)  $\left[ - 2 , \frac { 4 } { 3 } \right]$ 
A)  $( - \infty , - 2 ] \cup \left[ \frac { 4 } { 3 } , \infty \right]$ 
B)  $[ - 2 , \infty )$ 
C)  $\left[ - \infty , \frac { 4 } { 3 } \right]$ 
D)  $\left[ - 2 , \frac { 4 } { 3 } \right]$

Question 6

Fill in the blank with one of the words or phrases listed below.

-$\mathrm { A } ( \mathrm { n } )$ـــــــــــــــــ is an inequality that can be written so that one side is a quadratic expression and the other side is 0 .

Accepted Answer

A)  quadratic formula 
B)  quadratic inequality 
C)  discriminant 
D)  quadratic 
A)  quadratic formula 
B)  quadratic inequality 
C)  discriminant 
D)  quadratic

Question 7

Solve the inequality. Write the solution set in interval notation.
-$$x ^ { 4 } - 13 x ^ { 2 } + 36 \geq 0$$

Accepted Answer

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

Question 8

Solve the inequality. Write the solution set in interval notation.
-$$9 x ^ { 3 } + 36 x ^ { 2 } - 16 x - 64 > 0$$

Accepted Answer

A)  $\left( - 4 , - \frac { 4 } { 3 } \right) \cup \left( \frac { 4 } { 3 } , \infty \right)$ 
B)  $\left[ - 4 , - \frac { 4 } { 3 } \right] \cup \left[ \frac { 4 } { 3 } , \infty \right)$ 
C)  $( - \infty , - 4 ] \cup \left[ - \frac { 4 } { 3 } , \frac { 4 } { 3 } \right]$ 
D)  $( - \infty , - 4 ) \cup \left( - \frac { 4 } { 3 } , \frac { 4 } { 3 } \right)$ 
A)  $\left( - 4 , - \frac { 4 } { 3 } \right) \cup \left( \frac { 4 } { 3 } , \infty \right)$ 
B)  $\left[ - 4 , - \frac { 4 } { 3 } \right] \cup \left[ \frac { 4 } { 3 } , \infty \right)$ 
C)  $( - \infty , - 4 ] \cup \left[ - \frac { 4 } { 3 } , \frac { 4 } { 3 } \right]$ 
D)  $( - \infty , - 4 ) \cup \left( - \frac { 4 } { 3 } , \frac { 4 } { 3 } \right)$

Question 9

Solve.
-The profit that the vendor makes per day by selling $x$ pretzels is given by the function $P ( x ) = - 0.004 x ^ { 2 } + 2.4 x - 50$. Find the number of pretzels that must be sold to maximize profit.

Accepted Answer

A)  600 pretzels 
B)  300 pretzels 
C)  310 pretzels 
D)  $1.2$ pretzels 
A)  600 pretzels 
B)  300 pretzels 
C)  310 pretzels 
D)  $1.2$ pretzels

Question 10

Solve the equation by completing the square.
-$$2 x ^ { 2 } - 3 x = 5$$

Accepted Answer

A)  $\left\{ \frac { 5 } { 2 } , 1 \right\}$ 
B)  $\left\{ \frac { 5 } { 2 } , - 1 \right\}$ 
C)  $\left\{ \frac { 2 } { 5 } , - 1 \right\}$ 
D)  $\left\{ \frac { 2 } { 5 } , 1 \right\}$ 
A)  $\left\{ \frac { 5 } { 2 } , 1 \right\}$ 
B)  $\left\{ \frac { 5 } { 2 } , - 1 \right\}$ 
C)  $\left\{ \frac { 2 } { 5 } , - 1 \right\}$ 
D)  $\left\{ \frac { 2 } { 5 } , 1 \right\}$

Question 11

Use the square root property to solve the equation.
$4 x ^ { 2 } - 60 = 0$

Accepted Answer

A)  $\{ 30 \}$ 
B)  $\{ 16 \}$ 
C)  $\{ - 15,15 \}$ 
D)  $\{ - \sqrt { 15 } , \sqrt { 15 } \}$ 
A)  $\{ 30 \}$ 
B)  $\{ 16 \}$ 
C)  $\{ - 15,15 \}$ 
D)  $\{ - \sqrt { 15 } , \sqrt { 15 } \}$

Question 12

Solve the inequality. Write the solution set in interval notation.
-$$\frac { ( x + 11 ) ( x - 5 ) } { x - 1 } \geq 0$$

Accepted Answer

A)  $[ - 11,1 ) \cup [ 5 , \infty )$ 
B)  $[ - 11,1 ) \cup ( 1,5 ]$ 
C)  $( - \infty , - 11 ] \cup [ 5 , \infty )$ 
D)  $( - \infty , - 11 ] \cup ( 1,5 ]$ 
A)  $[ - 11,1 ) \cup [ 5 , \infty )$ 
B)  $[ - 11,1 ) \cup ( 1,5 ]$ 
C)  $( - \infty , - 11 ] \cup [ 5 , \infty )$ 
D)  $( - \infty , - 11 ] \cup ( 1,5 ]$

Question 13

Add the proper constant to the binomial so that the resulting trinomial is a perfect square trinomial. Then factor the
trinomial.
-$$y ^ { 2 } - 10 y$$

Accepted Answer

A)  $y ^ { 2 } - 10 y + 25 = ( y - 5 ) ^ { 2 }$ 
B)  $y ^ { 2 } - 10 y - 100 = ( y - 10 ) ^ { 2 }$ 
C)  $y ^ { 2 } - 10 y - 25 = ( y - 5 ) ^ { 2 }$ 
D)  $y ^ { 2 } - 10 y + 100 = ( y - 10 ) ^ { 2 }$ 
A)  $y ^ { 2 } - 10 y + 25 = ( y - 5 ) ^ { 2 }$ 
B)  $y ^ { 2 } - 10 y - 100 = ( y - 10 ) ^ { 2 }$ 
C)  $y ^ { 2 } - 10 y - 25 = ( y - 5 ) ^ { 2 }$ 
D)  $y ^ { 2 } - 10 y + 100 = ( y - 10 ) ^ { 2 }$

Question 14

Solve.
-The area of a rectangular wall in a classroom is 396 square feet. Its length is 3 feet shorter than three times its width. Find the length and width of the wall of the classroom.

Accepted Answer

A)  Width $= 12 \mathrm { ft }$; length $= 33 \mathrm { ft }$ 
B)  Width $= 12 \mathrm { ft }$; length $= 21 \mathrm { ft }$ 
C)  Width $= 12 \mathrm { ft }$; length $= 39 \mathrm { ft }$ 
D)  Width $= 12 \mathrm { ft }$; length $= 15 \mathrm { ft }$ 
A)  Width $= 12 \mathrm { ft }$; length $= 33 \mathrm { ft }$ 
B)  Width $= 12 \mathrm { ft }$; length $= 21 \mathrm { ft }$ 
C)  Width $= 12 \mathrm { ft }$; length $= 39 \mathrm { ft }$ 
D)  Width $= 12 \mathrm { ft }$; length $= 15 \mathrm { ft }$

Question 15

Use the discriminant to determine the number and type of solutions of the equation.
-$$x ^ { 2 } - 8 = 0$$

Accepted Answer

A)  Two real solutions 
B)  Two complex but not real solutions 
C)  One real solution 
A)  Two real solutions 
B)  Two complex but not real solutions 
C)  One real solution

Question 16

Find the vertex of the graph of the quadratic function. Find any intercepts and graph the function.
-$f ( x ) = - 3 x ^ { 2 } + 30 x - 79$

Accepted Answer

A)  Vertex: $( 5 , - 4 )$;
$x$-intercepts: none;
y-intercept: $( 0 , - 79 )$
  
B)  Vertex $( - 5 , - 4 )$;
$x$-intercepts: none;
$y$-intercept $( 0 , - 79 )$
  
C)  Vertex $( - 5 , - 4 )$;
x-intercepts: none;
y-intercept$\left( 0, - \frac { 37 } { 3 } \right)$;
  
D)  Vertex $( 5 , - 4 )$;
$\mathrm { x }$-intercepts: none;
$\mathrm { y }$-intercept: $\left( 0 , - \frac { 37 } { 3 } \right)$
  
A)  Vertex: $( 5 , - 4 )$;
$x$-intercepts: none;
y-intercept: $( 0 , - 79 )$
  
B)  Vertex $( - 5 , - 4 )$;
$x$-intercepts: none;
$y$-intercept $( 0 , - 79 )$
  
C)  Vertex $( - 5 , - 4 )$;
x-intercepts: none;
y-intercept$\left( 0, - \frac { 37 } { 3 } \right)$;
  
D)  Vertex $( 5 , - 4 )$;
$\mathrm { x }$-intercepts: none;
$\mathrm { y }$-intercept: $\left( 0 , - \frac { 37 } { 3 } \right)$

Question 17

Solve.
-$$x ^ { - 2 } + 8 x ^ { - 1 } + 7 = 0$$

Accepted Answer

A)  $\left\{ \frac { 1 } { 7 } , 1 \right\}$ 
B)  $\left\{ - \frac { 1 } { 7 } , - 1 \right\}$ 
C)  $\{ - 1 , - 7 \}$ 
D)  $\{ 1,7 \}$ 
A)  $\left\{ \frac { 1 } { 7 } , 1 \right\}$ 
B)  $\left\{ - \frac { 1 } { 7 } , - 1 \right\}$ 
C)  $\{ - 1 , - 7 \}$ 
D)  $\{ 1,7 \}$

Question 18

Solve the inequality. Write the solution set in interval notation.
-$$\left( x ^ { 2 } - 16 \right) \left( x ^ { 2 } - 1 \right) > 0$$

Accepted Answer

A)  $( - \infty , - 4 ] \cup [ - 1,1 ] \cup [ 4 , \infty )$ 
B)  $[ - 4 , - 1 ] \cup [ 1,4 ]$ 
C)  $( - 4 , - 1 ) \cup ( 1,4 )$ 
D)  $( - \infty , - 4 ) \cup ( - 1,1 ) \cup ( 4 , \infty )$ 
A)  $( - \infty , - 4 ] \cup [ - 1,1 ] \cup [ 4 , \infty )$ 
B)  $[ - 4 , - 1 ] \cup [ 1,4 ]$ 
C)  $( - 4 , - 1 ) \cup ( 1,4 )$ 
D)  $( - \infty , - 4 ) \cup ( - 1,1 ) \cup ( 4 , \infty )$

Question 19

Solve.
-The product of a number and 1 less than the number is 56. Find the number.

Accepted Answer

A)  -7 or 8 
B)  -9 or 6 
C)  -8 or 7 
D)  -6 or 9 
A)  -7 or 8 
B)  -9 or 6 
C)  -8 or 7 
D)  -6 or 9

Question 20

Solve.
-A ball is thrown downward with an initial velocity of 28 meters per second from a cliff that is 110 meters high. The height of the ball is given by the quadratic equation $h = - 4.9 t ^ { 2 } - 28 t + 110$ where $h$ is in meters and $t$ is the time in seconds since the ball was thrown. Find the time it takes the ball to hit the ground. Round your answer to the nearest tenth of a second.

Accepted Answer

A)  $2.6$ seconds 
B)  $2.8$ seconds 
C)  $3.7$ seconds 
D)  $2.7$ seconds 
A)  $2.6$ seconds 
B)  $2.8$ seconds 
C)  $3.7$ seconds 
D)  $2.7$ seconds

Use the quadratic formula to solve the equation. - $\frac { 1 } { 10 } x ^ { 2 } + x + 1 = 0$

Use the square root property to solve the equation. $( x + 2 ) ^ { 2 } = 17$

Solve the inequality. Write the solution set in interval notation. - $( x + 7 ) ( x - 1 ) ( x - 4 ) < 0$

Find the vertex of the graph of the quadratic function. Find any intercepts and graph the function. - $f ( x ) = 2 x ^ { 2 } + 8 x$ $Find the vertex of the graph of the quadratic function. Find any intercepts and graph the function. - f ( x ) = 2 x ^ { 2 } + 8 x$

Solve the inequality. Write the solution set in interval notation. - $( 3 x - 4 ) ( x + 2 ) \leq 0$

Solve the inequality. Write the solution set in interval notation. - $x ^ { 4 } - 13 x ^ { 2 } + 36 \geq 0$

Solve the inequality. Write the solution set in interval notation. - $9 x ^ { 3 } + 36 x ^ { 2 } - 16 x - 64 > 0$

Solve. -The profit that the vendor makes per day by selling $x$ pretzels is given by the function $P ( x ) = - 0.004 x ^ { 2 } + 2.4 x - 50$ . Find the number of pretzels that must be sold to maximize profit.

Solve the equation by completing the square. - $2 x ^ { 2 } - 3 x = 5$

Use the square root property to solve the equation. $4 x ^ { 2 } - 60 = 0$

Solve the inequality. Write the solution set in interval notation. - $\frac { ( x + 11 ) ( x - 5 ) } { x - 1 } \geq 0$

Add the proper constant to the binomial so that the resulting trinomial is a perfect square trinomial. Then factor the trinomial. - $y ^ { 2 } - 10 y$

Solve. -The area of a rectangular wall in a classroom is 396 square feet. Its length is 3 feet shorter than three times its width. Find the length and width of the wall of the classroom.

Use the discriminant to determine the number and type of solutions of the equation. - $x ^ { 2 } - 8 = 0$

Find the vertex of the graph of the quadratic function. Find any intercepts and graph the function. - $f ( x ) = - 3 x ^ { 2 } + 30 x - 79$ $Find the vertex of the graph of the quadratic function. Find any intercepts and graph the function. - f ( x ) = - 3 x ^ { 2 } + 30 x - 79$

Solve. - $x ^ { - 2 } + 8 x ^ { - 1 } + 7 = 0$

Solve the inequality. Write the solution set in interval notation. - $\left( x ^ { 2 } - 16 \right) \left( x ^ { 2 } - 1 \right) > 0$

Solve. -The product of a number and 1 less than the number is 56. Find the number.

Real Numbers and Algebraic Expressions

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Exam 8: Quadratic Equations and Functions

Use the quadratic formula to solve the equation. - 110x2+x+1=0\frac { 1 } { 10 } x ^ { 2 } + x + 1 = 0101​x2+x+1=0

Use the square root property to solve the equation. (x+2)2=17( x + 2 ) ^ { 2 } = 17(x+2)2=17

Solve the inequality. Write the solution set in interval notation. - (x+7)(x−1)(x−4)<0( x + 7 ) ( x - 1 ) ( x - 4 ) < 0(x+7)(x−1)(x−4)<0

Find the vertex of the graph of the quadratic function. Find any intercepts and graph the function. - f(x)=2x2+8xf ( x ) = 2 x ^ { 2 } + 8 xf(x)=2x2+8x

Solve the inequality. Write the solution set in interval notation. - (3x−4)(x+2)≤0( 3 x - 4 ) ( x + 2 ) \leq 0(3x−4)(x+2)≤0

Fill in the blank with one of the words or phrases listed below. - A(n)\mathrm { A } ( \mathrm { n } )A(n) ـــــــــــــــــ is an inequality that can be written so that one side is a quadratic expression and the other side is 0 .

Solve the inequality. Write the solution set in interval notation. - x4−13x2+36≥0x ^ { 4 } - 13 x ^ { 2 } + 36 \geq 0x4−13x2+36≥0

Solve the inequality. Write the solution set in interval notation. - 9x3+36x2−16x−64>09 x ^ { 3 } + 36 x ^ { 2 } - 16 x - 64 > 09x3+36x2−16x−64>0

Solve. -The profit that the vendor makes per day by selling xxx pretzels is given by the function P(x)=−0.004x2+2.4x−50P ( x ) = - 0.004 x ^ { 2 } + 2.4 x - 50P(x)=−0.004x2+2.4x−50 . Find the number of pretzels that must be sold to maximize profit.

Solve the equation by completing the square. - 2x2−3x=52 x ^ { 2 } - 3 x = 52x2−3x=5

Use the square root property to solve the equation. 4x2−60=04 x ^ { 2 } - 60 = 04x2−60=0

Solve the inequality. Write the solution set in interval notation. - (x+11)(x−5)x−1≥0\frac { ( x + 11 ) ( x - 5 ) } { x - 1 } \geq 0x−1(x+11)(x−5)​≥0

Add the proper constant to the binomial so that the resulting trinomial is a perfect square trinomial. Then factor the trinomial. - y2−10yy ^ { 2 } - 10 yy2−10y