Question 1

Solve the equation.
-$$x ^ { 2 } + 18 x + 59 = 0$$

Accepted Answer

A)  $\{ - 9 - \sqrt { 22 } , - 9 + \sqrt { 22 } \}$ 
B)  $\{ 9 - \sqrt { 59 } , 9 + \sqrt { 59 } \}$ 
C)  $\{ 9 + \sqrt { 22 } \}$ 
D)  $\{ - 18 + \sqrt { 59 } \}$ 
A)  $\{ - 9 - \sqrt { 22 } , - 9 + \sqrt { 22 } \}$ 
B)  $\{ 9 - \sqrt { 59 } , 9 + \sqrt { 59 } \}$ 
C)  $\{ 9 + \sqrt { 22 } \}$ 
D)  $\{ - 18 + \sqrt { 59 } \}$

Question 2

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

-The graph of $f ( x ) = a x ^ { 2 } + b x + c$, where $a$ is not 0 , is a parabola whose vertex has an $x$-value ofــــــــــــــــــ

Accepted Answer

A)  $( h , 0 )$ 
B)  $\pm \sqrt { b }$ 
C)  $( h , k )$ 
D)  $\frac { - b } { 2 a }$ 
A)  $( h , 0 )$ 
B)  $\pm \sqrt { b }$ 
C)  $( h , k )$ 
D)  $\frac { - b } { 2 a }$

Question 3

Match the function with its graph.
-$f ( x ) = x ^ { 2 } - 4 x$

Accepted Answer

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

Question 4

Find the vertex of the graph of the quadratic function. Find any intercepts and graph the function.
-$f ( x ) = - 2 x ^ { 2 } + 24 x - 70$

Accepted Answer

A)  Vertex: $( - 6,2 )$;
$x$-intercepts: $( - 5,0 )$ and $( - 7,0 )$;
y-intercept: $( 0 , - 70 )$
  
B)  Vertex: $( - 2 , - 6 )$;
$x$-intercepts: none;
y-intercept: $( 0 , - 70 )$
  
C)  Vertex: $( 6,6 )$;
$x$-intercepts: $( 6 \pm \sqrt { 3 } , 0 )$;
y-intercept: $( 0 , - 70 )$
  
D)  Vertex: $( 6,2 )$;
$x$-intercepts: $( 5,0 )$ and $( 7,0 )$;
$y$-intercept: $( 0 , - 70 )$
  
A)  Vertex: $( - 6,2 )$;
$x$-intercepts: $( - 5,0 )$ and $( - 7,0 )$;
y-intercept: $( 0 , - 70 )$
  
B)  Vertex: $( - 2 , - 6 )$;
$x$-intercepts: none;
y-intercept: $( 0 , - 70 )$
  
C)  Vertex: $( 6,6 )$;
$x$-intercepts: $( 6 \pm \sqrt { 3 } , 0 )$;
y-intercept: $( 0 , - 70 )$
  
D)  Vertex: $( 6,2 )$;
$x$-intercepts: $( 5,0 )$ and $( 7,0 )$;
$y$-intercept: $( 0 , - 70 )$

Question 5

Use the square root property to solve the equation.
$( x + 2 ) ^ { 2 } = 24$

Accepted Answer

A)  $\{ 2 \sqrt { 6 } - 2,2 \sqrt { 6 } + 2 \}$ 
B)  $\{ - 2 \sqrt { 6 } , 2 \sqrt { 6 } \}$ 
C)  $\{ - 2 - 2 \sqrt { 6 } , - 2 + 2 \sqrt { 6 } \}$ 
D)  $\{ - 2 - 2 \sqrt { 12 } , - 2 + 2 \sqrt { 12 } \}$ 
A)  $\{ 2 \sqrt { 6 } - 2,2 \sqrt { 6 } + 2 \}$ 
B)  $\{ - 2 \sqrt { 6 } , 2 \sqrt { 6 } \}$ 
C)  $\{ - 2 - 2 \sqrt { 6 } , - 2 + 2 \sqrt { 6 } \}$ 
D)  $\{ - 2 - 2 \sqrt { 12 } , - 2 + 2 \sqrt { 12 } \}$

Question 6

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

Accepted Answer

A)  Vertex: $( 1 , - 9 )$;
$x$-intercepts: $( - 2,0 )$ and $( 4,0 )$;
$y$-intercept: $( 0 , - 8 )$
  
B)  Vertex: $( - 1 , - 9 )$;
$x$-intercepts: $( - 4,0 )$ and $( 2,0 )$;
$y$-intercept: $( 0 , - 8 )$
  
C)  Vertex: $( - 1 , - 9 )$;
x-intercepts: $( - 4,0 )$ and $( 2,0 )$;
y-intercept: $( 0,8 )$
  
D)  Vertex: $( 1 , - 9 )$;
$x$-intercepts: $( 2,0 )$ and $( 4,0 )$;
$y$-intercept: $( 0 , - 8 )$
  
A)  Vertex: $( 1 , - 9 )$;
$x$-intercepts: $( - 2,0 )$ and $( 4,0 )$;
$y$-intercept: $( 0 , - 8 )$
  
B)  Vertex: $( - 1 , - 9 )$;
$x$-intercepts: $( - 4,0 )$ and $( 2,0 )$;
$y$-intercept: $( 0 , - 8 )$
  
C)  Vertex: $( - 1 , - 9 )$;
x-intercepts: $( - 4,0 )$ and $( 2,0 )$;
y-intercept: $( 0,8 )$
  
D)  Vertex: $( 1 , - 9 )$;
$x$-intercepts: $( 2,0 )$ and $( 4,0 )$;
$y$-intercept: $( 0 , - 8 )$

Question 7

Solve.
-A rectangular sign must have an area of 18 square yards. Its length must be 6 yards more than its width. Find the dimensions of the sign.

Accepted Answer

A)  $3 + 3 \sqrt { 3 }$ yards by $- 3 + 3 \sqrt { 3 }$ yards 
B)  $3 + 3 \sqrt { 3 }$ yards by $9 + 3 \sqrt { 3 }$ yards 
C)  $3 - 3 \sqrt { 3 }$ yards by $3 + 3 \sqrt { 3 }$ yards 
D)  $3 - 3 \sqrt { 3 }$ yards by $- 3 - 3 \sqrt { 3 }$ yards 
A)  $3 + 3 \sqrt { 3 }$ yards by $- 3 + 3 \sqrt { 3 }$ yards 
B)  $3 + 3 \sqrt { 3 }$ yards by $9 + 3 \sqrt { 3 }$ yards 
C)  $3 - 3 \sqrt { 3 }$ yards by $3 + 3 \sqrt { 3 }$ yards 
D)  $3 - 3 \sqrt { 3 }$ yards by $- 3 - 3 \sqrt { 3 }$ yards

Question 8

Solve.
-$$\frac { 7 } { x - 1 } + \frac { x } { x + 1 } = \frac { 10 } { x ^ { 2 } - 1 }$$

Accepted Answer

A)  $\{ 3 - \sqrt { 6 } , 3 + \sqrt { 6 } \}$ 
B)  $\{ - 3 - 2 \sqrt { 3 } , - 3 + 2 \sqrt { 3 } \}$ 
C)  $\{ - 3 - \sqrt { 6 } , - 3 + \sqrt { 6 } \}$ 
D)  $\{ 3 - 2 \sqrt { 3 } , 3 + 2 \sqrt { 3 } \}$ 
A)  $\{ 3 - \sqrt { 6 } , 3 + \sqrt { 6 } \}$ 
B)  $\{ - 3 - 2 \sqrt { 3 } , - 3 + 2 \sqrt { 3 } \}$ 
C)  $\{ - 3 - \sqrt { 6 } , - 3 + \sqrt { 6 } \}$ 
D)  $\{ 3 - 2 \sqrt { 3 } , 3 + 2 \sqrt { 3 } \}$

Question 9

Solve the inequality. Write the solution set in interval notation.
-$$\frac { 2 x } { x + 7 } < x$$

Accepted Answer

A)  $( - 7 , - 5 ) \cup ( 0 , \infty )$ 
B)  $( - \infty , 5 ) \cup ( 7 , \infty )$ 
C)  $( - \infty , - 7 ) \cup ( - 5,0 )$ 
D)  $( - \infty , - 7 ) \cup ( 0 , \infty )$ 
A)  $( - 7 , - 5 ) \cup ( 0 , \infty )$ 
B)  $( - \infty , 5 ) \cup ( 7 , \infty )$ 
C)  $( - \infty , - 7 ) \cup ( - 5,0 )$ 
D)  $( - \infty , - 7 ) \cup ( 0 , \infty )$

Question 10

Add the proper constant to the binomial so that the resulting trinomial is a perfect square trinomial. Then factor the
trinomial.
-$$\mathrm { p } ^ { 2 } + 5 \mathrm { p }$$

Accepted Answer

A)  $p ^ { 2 } + 5 p + \frac { 25 } { 4 } = \left( p + \frac { 5 } { 2 } \right) ^ { 2 }$ 
B)  $\mathrm { p } ^ { 2 } + 5 \mathrm { p } - \frac { 25 } { 4 } = \left( \mathrm { p } - \frac { 5 } { 2 } \right) ^ { 2 }$ 
C)  $p ^ { 2 } + 5 p + 10 = ( p + 5 ) ^ { 2 }$ 
D)  $p ^ { 2 } + 5 p + \frac { 25 } { 2 } = \left( p + \frac { 25 } { 2 } \right) ^ { 2 }$ 
A)  $p ^ { 2 } + 5 p + \frac { 25 } { 4 } = \left( p + \frac { 5 } { 2 } \right) ^ { 2 }$ 
B)  $\mathrm { p } ^ { 2 } + 5 \mathrm { p } - \frac { 25 } { 4 } = \left( \mathrm { p } - \frac { 5 } { 2 } \right) ^ { 2 }$ 
C)  $p ^ { 2 } + 5 p + 10 = ( p + 5 ) ^ { 2 }$ 
D)  $p ^ { 2 } + 5 p + \frac { 25 } { 2 } = \left( p + \frac { 25 } { 2 } \right) ^ { 2 }$

Question 11

Solve.
-An isosceles right triangle has legs of equal length. If the hypotenuse is 22 inches long, find the length of each leg.

Accepted Answer

A)  $\frac { 11 } { 2 } \sqrt { 2 } \mathrm { in }$. 
B)  $22 \sqrt { 2 } \mathrm { in }$. 
C)  $121 \sqrt { 2 } \mathrm { in }$. 
D)  $11 \sqrt { 2 } \mathrm { in }$. 
A)  $\frac { 11 } { 2 } \sqrt { 2 } \mathrm { in }$. 
B)  $22 \sqrt { 2 } \mathrm { in }$. 
C)  $121 \sqrt { 2 } \mathrm { in }$. 
D)  $11 \sqrt { 2 } \mathrm { in }$.

Question 12

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

Accepted Answer

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

Question 13

Use the discriminant to determine the number and type of solutions of the equation.
-$$10 - 8 x ^ { 2 } = - 6 x + 9$$

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 14

Solve the equation.
-$$x ^ { 6 } + 9 = 9 x ^ { 4 } + x ^ { 2 }$$

Accepted Answer

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

Question 15

Use the quadratic formula and a calculator to approximate the solution to the nearest tenth.
-$$- 2 x ^ { 2 } + 6 x + 3 = 0$$

Accepted Answer

A)  $\{ - 3.4,0.4 \}$ 
B)  $\{ - 0.9,6.9 \}$ 
C)  $\{ - 0.4,3.4 \}$ 
D)  $\{ - 13.5,16.5 \}$ 
A)  $\{ - 3.4,0.4 \}$ 
B)  $\{ - 0.9,6.9 \}$ 
C)  $\{ - 0.4,3.4 \}$ 
D)  $\{ - 13.5,16.5 \}$

Question 16

Match the function with its graph.
-$f ( x ) = x ^ { 2 } - 4$

Accepted Answer

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

Question 17

Add the proper constant to the binomial so that the resulting trinomial is a perfect square trinomial. Then factor the
trinomial.
-$$x ^ { 2 } - \frac { 2 } { 9 } x$$

Accepted Answer

A)  $x ^ { 2 } - \frac { 2 } { 9 } x + \frac { 2 } { 81 } = \left( x - \frac { 1 } { 9 } \right) ^ { 2 }$ 
B)  $x ^ { 2 } - \frac { 2 } { 9 } x + \frac { 1 } { 81 } = \left( x - \frac { 1 } { 9 } \right) ^ { 2 }$ 
C)  $x ^ { 2 } - \frac { 2 } { 9 } x + \frac { 1 } { 81 } = \left( x + \frac { 1 } { 9 } \right) ^ { 2 }$ 
D)  $x ^ { 2 } - \frac { 2 } { 9 } x + \frac { 4 } { 81 } = \left( x - \frac { 2 } { 9 } \right) ^ { 2 }$ 
A)  $x ^ { 2 } - \frac { 2 } { 9 } x + \frac { 2 } { 81 } = \left( x - \frac { 1 } { 9 } \right) ^ { 2 }$ 
B)  $x ^ { 2 } - \frac { 2 } { 9 } x + \frac { 1 } { 81 } = \left( x - \frac { 1 } { 9 } \right) ^ { 2 }$ 
C)  $x ^ { 2 } - \frac { 2 } { 9 } x + \frac { 1 } { 81 } = \left( x + \frac { 1 } { 9 } \right) ^ { 2 }$ 
D)  $x ^ { 2 } - \frac { 2 } { 9 } x + \frac { 4 } { 81 } = \left( x - \frac { 2 } { 9 } \right) ^ { 2 }$

Question 18

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

Accepted Answer

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

Question 19

Solve the inequality. Write the solution set in interval notation.
-$$x ^ { 2 } + 5 x \geq - 4$$

Accepted Answer

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

Question 20

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

Accepted Answer

A)  Vertex: $( - 1,9 )$;
$x$-intercepts: $( - 2,0 )$ and $( 4,0 )$;
$y$-intercept: $( 0,8 )$
  
B)  Vertex: $( - 1 , - 9 )$;
$x$-intercepts: $( - 4,0 )$ and $( 2,0 )$;
$y$-intercept: $( 0,8 )$
  
C)  Vertex: $( - 1,9 )$;
x-intercepts: $( - 4,0 )$ and $( 2,0 )$;
$y$-intercept: $( 0,8 )$
  
D)  Vertex: $( 1,9 )$;
x-intercepts: $( - 2,0 )$ and $( 4,0 )$;
y-intercept: $( 0,8 )$
  
A)  Vertex: $( - 1,9 )$;
$x$-intercepts: $( - 2,0 )$ and $( 4,0 )$;
$y$-intercept: $( 0,8 )$
  
B)  Vertex: $( - 1 , - 9 )$;
$x$-intercepts: $( - 4,0 )$ and $( 2,0 )$;
$y$-intercept: $( 0,8 )$
  
C)  Vertex: $( - 1,9 )$;
x-intercepts: $( - 4,0 )$ and $( 2,0 )$;
$y$-intercept: $( 0,8 )$
  
D)  Vertex: $( 1,9 )$;
x-intercepts: $( - 2,0 )$ and $( 4,0 )$;
y-intercept: $( 0,8 )$

Solve the equation. - $x ^ { 2 } + 18 x + 59 = 0$

Match the function with its graph. - $f ( x ) = x ^ { 2 } - 4 x$

Find the vertex of the graph of the quadratic function. Find any intercepts and graph the function. - $f ( x ) = - 2 x ^ { 2 } + 24 x - 70$ $Find the vertex of the graph of the quadratic function. Find any intercepts and graph the function. - f ( x ) = - 2 x ^ { 2 } + 24 x - 70$

Use the square root property to solve the equation. $( x + 2 ) ^ { 2 } = 24$

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

Solve. -A rectangular sign must have an area of 18 square yards. Its length must be 6 yards more than its width. Find the dimensions of the sign.

Solve. - $\frac { 7 } { x - 1 } + \frac { x } { x + 1 } = \frac { 10 } { x ^ { 2 } - 1 }$

Solve the inequality. Write the solution set in interval notation. - $\frac { 2 x } { x + 7 } < x$

Add the proper constant to the binomial so that the resulting trinomial is a perfect square trinomial. Then factor the trinomial. - $\mathrm { p } ^ { 2 } + 5 \mathrm { p }$

Solve. -An isosceles right triangle has legs of equal length. If the hypotenuse is 22 inches long, find the length of each leg.

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

Use the discriminant to determine the number and type of solutions of the equation. - $10 - 8 x ^ { 2 } = - 6 x + 9$

Solve the equation. - $x ^ { 6 } + 9 = 9 x ^ { 4 } + x ^ { 2 }$

Use the quadratic formula and a calculator to approximate the solution to the nearest tenth. - $- 2 x ^ { 2 } + 6 x + 3 = 0$

Match the function with its graph. - $f ( x ) = x ^ { 2 } - 4$

Add the proper constant to the binomial so that the resulting trinomial is a perfect square trinomial. Then factor the trinomial. - $x ^ { 2 } - \frac { 2 } { 9 } x$

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

Solve the inequality. Write the solution set in interval notation. - $x ^ { 2 } + 5 x \geq - 4$

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

Real Numbers and Algebraic Expressions

Equations, Inequalities, and Problem Solving

Graphs and Functions

Systems of Equations and Inequalities

Polynomials and Polynomial Functions

Rational Expressions

Rational Exponents, Radicals, and Complex Numbers

Exponential and Logarithmic Functions

Conic Sections

Fractions

Filters

Exam 8: Quadratic Equations and Functions

Solve the equation. - x2+18x+59=0x ^ { 2 } + 18 x + 59 = 0x2+18x+59=0

Fill in the blank with one of the words or phrases listed below. -The graph of f(x)=ax2+bx+cf ( x ) = a x ^ { 2 } + b x + cf(x)=ax2+bx+c , where aaa is not 0 , is a parabola whose vertex has an xxx -value ofــــــــــــــــــ

Match the function with its graph. - f(x)=x2−4xf ( x ) = x ^ { 2 } - 4 xf(x)=x2−4x

Find the vertex of the graph of the quadratic function. Find any intercepts and graph the function. - f(x)=−2x2+24x−70f ( x ) = - 2 x ^ { 2 } + 24 x - 70f(x)=−2x2+24x−70

Use the square root property to solve the equation. (x+2)2=24( x + 2 ) ^ { 2 } = 24(x+2)2=24

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