Question 1

Solve the equation by completing the square.
-$x ^ { 2 } + 41 = - 16 x$

Accepted Answer

A)  $8 + \sqrt { 23 }$ 
B)  $- 8 - \sqrt { 23 } , - 8 + \sqrt { 23 }$ 
C)  $8 - \sqrt { 41 } , 8 + \sqrt { 41 }$ 
D)  $- 16 + \sqrt { 41 }$ 
A)  $8 + \sqrt { 23 }$ 
B)  $- 8 - \sqrt { 23 } , - 8 + \sqrt { 23 }$ 
C)  $8 - \sqrt { 41 } , 8 + \sqrt { 41 }$ 
D)  $- 16 + \sqrt { 41 }$

Question 2

Solve the equation.
-$\mathrm { u } ^ { 2 } + 14 \mathrm { u } + 39 = 0$

Accepted Answer

A)  $7 - \sqrt { 39 } , 7 + \sqrt { 39 }$ 
B)  $- 7 - \sqrt { 10 } , - 7 + \sqrt { 10 }$ 
C)  $- 14 + \sqrt { 39 }$ 
D)  $7 + \sqrt { 10 }$ 
A)  $7 - \sqrt { 39 } , 7 + \sqrt { 39 }$ 
B)  $- 7 - \sqrt { 10 } , - 7 + \sqrt { 10 }$ 
C)  $- 14 + \sqrt { 39 }$ 
D)  $7 + \sqrt { 10 }$

Question 3

Solve.
-$4 x = \sqrt { 9 x + 2 }$

Accepted Answer

A)  $\frac { 9 + \sqrt { 209 } } { 32 }$ 
B)  $\frac { 9 + i \sqrt { 47 } } { 32 }$ 
C)  $\frac { - 9 - \sqrt { 209 } } { 32 } , \frac { - 9 + \sqrt { 209 } } { 32 }$ 
D)  $\frac { 9 - \sqrt { 209 } } { 32 } , \frac { 9 + \sqrt { 209 } } { 32 }$ 
A)  $\frac { 9 + \sqrt { 209 } } { 32 }$ 
B)  $\frac { 9 + i \sqrt { 47 } } { 32 }$ 
C)  $\frac { - 9 - \sqrt { 209 } } { 32 } , \frac { - 9 + \sqrt { 209 } } { 32 }$ 
D)  $\frac { 9 - \sqrt { 209 } } { 32 } , \frac { 9 + \sqrt { 209 } } { 32 }$

Question 4

Solve the equation.
-$y ^ { 2 } - 3 y = 2$

Accepted Answer

A)  $\frac { 3 + \sqrt { 17 } } { 2 } , \frac { 3 - \sqrt { 17 } } { 2 }$ 
B)  $\varnothing$ 
C)  $\frac { - 3 + \sqrt { 17 } } { 2 } , \frac { - 3 - \sqrt { 17 } } { 2 }$ 
D)  $\frac { 3 + i \sqrt { 17 } } { 2 } , \frac { 3 - i \sqrt { 17 } } { 2 }$ 
A)  $\frac { 3 + \sqrt { 17 } } { 2 } , \frac { 3 - \sqrt { 17 } } { 2 }$ 
B)  $\varnothing$ 
C)  $\frac { - 3 + \sqrt { 17 } } { 2 } , \frac { - 3 - \sqrt { 17 } } { 2 }$ 
D)  $\frac { 3 + i \sqrt { 17 } } { 2 } , \frac { 3 - i \sqrt { 17 } } { 2 }$

Question 5

Solve.
-Suppose that an open box is to be made from a square sheet of cardboard by cutting out 2 -inch squares from each corner as shown and then folding along the dotted lines. If the box is to have a volume of 50 cubic inches, find the original dimensions of the sheet of cardboard.

Accepted Answer

A)  $\sqrt { 5 } \mathrm { in. }$ by $\sqrt { 10 } \mathrm { in }$. 
B)  $5 \sqrt { 2 }$ in. by $5 \sqrt { 2 }$ in. 
C)  5 in. by $5 \mathrm { in }$. 
D)  9 in. by $9 \mathrm { in }$. 
A)  $\sqrt { 5 } \mathrm { in. }$ by $\sqrt { 10 } \mathrm { in }$. 
B)  $5 \sqrt { 2 }$ in. by $5 \sqrt { 2 }$ in. 
C)  5 in. by $5 \mathrm { in }$. 
D)  9 in. by $9 \mathrm { in }$.

Question 6

Find the vertex of the graph of the quadratic function.
-$f ( x ) = x ^ { 2 } + x + 5$

Accepted Answer

A)  $( - 1,5 )$ 
B)  $\left( - \frac { 1 } { 2 } , \frac { 19 } { 4 } \right)$ 
C)  $\left( \frac { 1 } { 2 } , \frac { 23 } { 4 } \right)$ 
D)  $( 1,7 )$ 
A)  $( - 1,5 )$ 
B)  $\left( - \frac { 1 } { 2 } , \frac { 19 } { 4 } \right)$ 
C)  $\left( \frac { 1 } { 2 } , \frac { 23 } { 4 } \right)$ 
D)  $( 1,7 )$

Question 7

Solve.
-$x ^ { 4 } - 625 = 0$

Accepted Answer

A)  $- 25,25 , - 25 i , 25 i$ 
B)  $- 25,25$ 
C)  $- 5,5 , - 5 i$, $5 \mathrm { i }$ 
D)  $- 5,5$ 
A)  $- 25,25 , - 25 i , 25 i$ 
B)  $- 25,25$ 
C)  $- 5,5 , - 5 i$, $5 \mathrm { i }$ 
D)  $- 5,5$

Question 8

Sketch the graph of the quadratic function by finding the vertex, intercepts, and determining if the graph opens upward
or downward.
-$f(x)=-x^{2}-6 x$

Accepted Answer

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

Question 9

Use the quadratic formula to solve the equation.
-$\frac { z ^ { 2 } } { - 4 } = \frac { z } { 7 } + \frac { 3 } { - 28 }$

Accepted Answer

A)  $\frac { 3 } { 7 }$ 
B)  $- \frac { 3 } { 7 } , 1$ 
C)  $- 1 , \frac { 3 } { 7 }$ 
D)  $- \frac { 3 } { 7 } , - 1$ 
A)  $\frac { 3 } { 7 }$ 
B)  $- \frac { 3 } { 7 } , 1$ 
C)  $- 1 , \frac { 3 } { 7 }$ 
D)  $- \frac { 3 } { 7 } , - 1$

Question 10

Match the function with its graph.
-$f ( x ) = - x ^ { 2 } + 1$

Accepted Answer

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

Question 11

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

Accepted Answer

A)  vertex $( 0 , - 5 )$; axis $x = 0$
  
B)  vertex $( 5,0 )$; axis $x = 5$
  
C)  vertex $( 0,5 )$; axis $x = 0$
  
D)  vertex $( - 5,0 )$; axis $x = - 5$
  
A)  vertex $( 0 , - 5 )$; axis $x = 0$
  
B)  vertex $( 5,0 )$; axis $x = 5$
  
C)  vertex $( 0,5 )$; axis $x = 0$
  
D)  vertex $( - 5,0 )$; axis $x = - 5$

Question 12

Solve the inequality. Graph the solution set and write the solution set in interval notation.
-$x ^ { 2 } - 3 x - 18 \leq 0$

Accepted Answer

A)  $( - \infty , - 3 ] \cup [ 6 , \infty )$
  
B)  $[ - 3,6 ]$
  
C) $[ 6 , \infty )$
  
D)  $( - \infty , - 3 ]$
  
A)  $( - \infty , - 3 ] \cup [ 6 , \infty )$
  
B)  $[ - 3,6 ]$
  
C) $[ 6 , \infty )$
  
D)  $( - \infty , - 3 ]$

Question 13

Use the quadratic formula to solve the equation.
-$9 x ^ { 2 } + 5 x + 2 = 0$

Accepted Answer

A)  $\frac { 5 - \sqrt { 47 } } { 18 } , \frac { 5 + \sqrt { 47 } } { 18 }$ 
B)  $\frac { 5 - i \sqrt { 47 } } { 18 } , \frac { 5 + i \sqrt { 47 } } { 18 }$ 
C)  $\frac { - 5 - i \sqrt { 47 } } { 18 } , \frac { - 5 + i \sqrt { 47 } } { 18 }$ 
D)  $\frac { - 5 - \sqrt { 47 } } { 18 } , \frac { - 5 + \sqrt { 47 } } { 18 }$ 
A)  $\frac { 5 - \sqrt { 47 } } { 18 } , \frac { 5 + \sqrt { 47 } } { 18 }$ 
B)  $\frac { 5 - i \sqrt { 47 } } { 18 } , \frac { 5 + i \sqrt { 47 } } { 18 }$ 
C)  $\frac { - 5 - i \sqrt { 47 } } { 18 } , \frac { - 5 + i \sqrt { 47 } } { 18 }$ 
D)  $\frac { - 5 - \sqrt { 47 } } { 18 } , \frac { - 5 + \sqrt { 47 } } { 18 }$

Question 14

Solve.
-The profit that the vendor makes per day by selling $x$ pretzels is given by the function $P ( x ) = - 0.002 x ^ { 2 } + 1.6 x - 150$. Find the number of pretzels that must be sold to maximize profit.

Accepted Answer

A)  800 pretzels 
B)  400 pretzels 
C)  $0.8$ pretzels 
D)  170 pretzels 
A)  800 pretzels 
B)  400 pretzels 
C)  $0.8$ pretzels 
D)  170 pretzels

Question 15

Solve.
-The length and width of a rectangle must have a sum of 68 feet. Find the dimensions of the rectangle whose area is as large as possible.

Accepted Answer

A)  length $34 \mathrm { ft }$; width $34 \mathrm { ft }$ 
B)  length $34 \mathrm { ft }$; width $102 \mathrm { ft }$ 
C)  length $33 \mathrm { ft }$; width $35 \mathrm { ft }$ 
D)  length $\frac { 1 } { 34 } \mathrm { ft }$; width $\frac { 13 } { 34 } \mathrm { ft }$ 
A)  length $34 \mathrm { ft }$; width $34 \mathrm { ft }$ 
B)  length $34 \mathrm { ft }$; width $102 \mathrm { ft }$ 
C)  length $33 \mathrm { ft }$; width $35 \mathrm { ft }$ 
D)  length $\frac { 1 } { 34 } \mathrm { ft }$; width $\frac { 13 } { 34 } \mathrm { ft }$

Question 16

Solve the equation by completing the square.
-$16 x ^ { 2 } - 5 x + 1 = 0$

Accepted Answer

A)  $\frac { 5 - i \sqrt { 39 } } { 32 } , \frac { 5 + i \sqrt { 39 } } { 32 }$ 
B)  $\frac { 5 - \mathrm { i } \sqrt { 39 } } { 32 } , \frac { - 5 + \mathrm { i } \sqrt { 39 } } { 32 }$ 
C)  $\frac { - 5 - i \sqrt { 39 } } { 32 } , \frac { - 5 + i \sqrt { 39 } } { 32 }$ 
D)  $\frac { - 5 - \mathrm { i } \sqrt { 39 } } { 32 } , \frac { 5 + \mathrm { i } \sqrt { 39 } } { 32 }$ 
A)  $\frac { 5 - i \sqrt { 39 } } { 32 } , \frac { 5 + i \sqrt { 39 } } { 32 }$ 
B)  $\frac { 5 - \mathrm { i } \sqrt { 39 } } { 32 } , \frac { - 5 + \mathrm { i } \sqrt { 39 } } { 32 }$ 
C)  $\frac { - 5 - i \sqrt { 39 } } { 32 } , \frac { - 5 + i \sqrt { 39 } } { 32 }$ 
D)  $\frac { - 5 - \mathrm { i } \sqrt { 39 } } { 32 } , \frac { 5 + \mathrm { i } \sqrt { 39 } } { 32 }$

Question 17

Match the function with its graph.
-$f ( x ) = x ^ { 2 } + 6 x + 8$

Accepted Answer

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

Question 18

Graph the function. Find the vertex.
-$f(x)=5 x^{2}$

Accepted Answer

A)  vertex: $( 0,0 )$
  
B)  vertex: $( 0,5 )$
  
C)  vertex: $( 0,0 )$
  
D)  vertex: $( 0,0 )$
  
A)  vertex: $( 0,0 )$
  
B)  vertex: $( 0,5 )$
  
C)  vertex: $( 0,0 )$
  
D)  vertex: $( 0,0 )$

Question 19

Solve the equation by completing the square.
-$x ^ { 2 } + 14 x + 74 = 0$

Accepted Answer

A)  $- 7 + 5 i$ 
B)  $- 7 - 25 i , - 7 + 25 i$ 
C)  $- 2 , - 12$ 
D)  $- 7 + 5 i , - 7 - 5 i$ 
A)  $- 7 + 5 i$ 
B)  $- 7 - 25 i , - 7 + 25 i$ 
C)  $- 2 , - 12$ 
D)  $- 7 + 5 i , - 7 - 5 i$

Question 20

Use the quadratic formula to solve the equation.
-$x ^ { 2 } - 5 x + 4 = 0$

Accepted Answer

A)  $- 4,1$ 
B)  $- 4 , - 1$ 
C)  4,1 
D)  4,0 
A)  $- 4,1$ 
B)  $- 4 , - 1$ 
C)  4,1 
D)  4,0

Solve the equation by completing the square. - $x ^ { 2 } + 41 = - 16 x$

Solve the equation. - $\mathrm { u } ^ { 2 } + 14 \mathrm { u } + 39 = 0$

Solve. - $4 x = \sqrt { 9 x + 2 }$

Solve the equation. - $y ^ { 2 } - 3 y = 2$

Solve. -Suppose that an open box is to be made from a square sheet of cardboard by cutting out 2 -inch squares from each corner as shown and then folding along the dotted lines. If the box is to have a volume of 50 cubic inches, find the original dimensions of the sheet of cardboard.

Find the vertex of the graph of the quadratic function. - $f ( x ) = x ^ { 2 } + x + 5$

Solve. - $x ^ { 4 } - 625 = 0$

Use the quadratic formula to solve the equation. - $\frac { z ^ { 2 } } { - 4 } = \frac { z } { 7 } + \frac { 3 } { - 28 }$

Match the function with its graph. - $f ( x ) = - x ^ { 2 } + 1$

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

Solve the inequality. Graph the solution set and write the solution set in interval notation. - $x ^ { 2 } - 3 x - 18 \leq 0$ $Solve the inequality. Graph the solution set and write the solution set in interval notation. - x ^ { 2 } - 3 x - 18 \leq 0$

Use the quadratic formula to solve the equation. - $9 x ^ { 2 } + 5 x + 2 = 0$

Solve. -The profit that the vendor makes per day by selling $x$ pretzels is given by the function $P ( x ) = - 0.002 x ^ { 2 } + 1.6 x - 150$ . Find the number of pretzels that must be sold to maximize profit.

Solve. -The length and width of a rectangle must have a sum of 68 feet. Find the dimensions of the rectangle whose area is as large as possible.

Solve the equation by completing the square. - $16 x ^ { 2 } - 5 x + 1 = 0$

Match the function with its graph. - $f ( x ) = x ^ { 2 } + 6 x + 8$

Graph the function. Find the vertex. - $f(x)=5 x^{2}$ $Graph the function. Find the vertex. - f(x)=5 x^{2}$

Solve the equation by completing the square. - $x ^ { 2 } + 14 x + 74 = 0$

Use the quadratic formula to solve the equation. - $x ^ { 2 } - 5 x + 4 = 0$

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

Solve the equation by completing the square. - x2+41=−16xx ^ { 2 } + 41 = - 16 xx2+41=−16x

Solve the equation. - u2+14u+39=0\mathrm { u } ^ { 2 } + 14 \mathrm { u } + 39 = 0u2+14u+39=0

Solve. - 4x=9x+24 x = \sqrt { 9 x + 2 }4x=9x+2​

Solve the equation. - y2−3y=2y ^ { 2 } - 3 y = 2y2−3y=2

Solve. -Suppose that an open box is to be made from a square sheet of cardboard by cutting out 2 -inch squares from each corner as shown and then folding along the dotted lines. If the box is to have a volume of 50 cubic inches, find the original dimensions of the sheet of cardboard.

Find the vertex of the graph of the quadratic function. - f(x)=x2+x+5f ( x ) = x ^ { 2 } + x + 5f(x)=x2+x+5

Solve. - x4−625=0x ^ { 4 } - 625 = 0x4−625=0

Sketch the graph of the quadratic function by finding the vertex, intercepts, and determining if the graph opens upward or downward. - f(x)=−x2−6xf(x)=-x^{2}-6 xf(x)=−x2−6x

Use the quadratic formula to solve the equation. - z2−4=z7+3−28\frac { z ^ { 2 } } { - 4 } = \frac { z } { 7 } + \frac { 3 } { - 28 }−4z2​=7z​+−283​

Match the function with its graph. - f(x)=−x2+1f ( x ) = - x ^ { 2 } + 1f(x)=−x2+1

Sketch the graph of the quadratic function. Give the vertex and axis of symmetry. - f(x)=−(x−5)2f(x)=-(x-5)^{2}f(x)=−(x−5)2

Solve the inequality. Graph the solution set and write the solution set in interval notation. - x2−3x−18≤0x ^ { 2 } - 3 x - 18 \leq 0x2−3x−18≤0

Use the quadratic formula to solve the equation. - 9x2+5x+2=09 x ^ { 2 } + 5 x + 2 = 09x2+5x+2=0

Solve. -The profit that the vendor makes per day by selling xxx pretzels is given by the function P(x)=−0.002x2+1.6x−150P ( x ) = - 0.002 x ^ { 2 } + 1.6 x - 150P(x)=−0.002x2+1.6x−150 . Find the number of pretzels that must be sold to maximize profit.

Solve. -The length and width of a rectangle must have a sum of 68 feet. Find the dimensions of the rectangle whose area is as large as possible.

Solve the equation by completing the square. - 16x2−5x+1=016 x ^ { 2 } - 5 x + 1 = 016x2−5x+1=0

Match the function with its graph. - f(x)=x2+6x+8f ( x ) = x ^ { 2 } + 6 x + 8f(x)=x2+6x+8

Graph the function. Find the vertex. - f(x)=5x2f(x)=5 x^{2}f(x)=5x2

Solve the equation by completing the square. - x2+14x+74=0x ^ { 2 } + 14 x + 74 = 0x2+14x+74=0

Use the quadratic formula to solve the equation. - x2−5x+4=0x ^ { 2 } - 5 x + 4 = 0x2−5x+4=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

Solve the equation by completing the square. - $x ^ { 2 } + 41 = - 16 x$

Solve the equation. - $\mathrm { u } ^ { 2 } + 14 \mathrm { u } + 39 = 0$

Solve. - $4 x = \sqrt { 9 x + 2 }$

Solve the equation. - $y ^ { 2 } - 3 y = 2$

Find the vertex of the graph of the quadratic function. - $f ( x ) = x ^ { 2 } + x + 5$

Solve. - $x ^ { 4 } - 625 = 0$

Use the quadratic formula to solve the equation. - $\frac { z ^ { 2 } } { - 4 } = \frac { z } { 7 } + \frac { 3 } { - 28 }$

Match the function with its graph. - $f ( x ) = - x ^ { 2 } + 1$

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

Solve the inequality. Graph the solution set and write the solution set in interval notation. - $x ^ { 2 } - 3 x - 18 \leq 0$ $Solve the inequality. Graph the solution set and write the solution set in interval notation. - x ^ { 2 } - 3 x - 18 \leq 0$

Use the quadratic formula to solve the equation. - $9 x ^ { 2 } + 5 x + 2 = 0$

Solve. -The profit that the vendor makes per day by selling $x$ pretzels is given by the function $P ( x ) = - 0.002 x ^ { 2 } + 1.6 x - 150$ . Find the number of pretzels that must be sold to maximize profit.

Solve the equation by completing the square. - $16 x ^ { 2 } - 5 x + 1 = 0$

Match the function with its graph. - $f ( x ) = x ^ { 2 } + 6 x + 8$

Graph the function. Find the vertex. - $f(x)=5 x^{2}$ $Graph the function. Find the vertex. - f(x)=5 x^{2}$

Solve the equation by completing the square. - $x ^ { 2 } + 14 x + 74 = 0$

Use the quadratic formula to solve the equation. - $x ^ { 2 } - 5 x + 4 = 0$