Question 1

The solutions of $a x ^ { 2 } + b x + c = 0$  $( a \neq 0 )$ are

Accepted Answer

A)  $x = - b \pm \frac { \sqrt { b ^ { 2 } - 4 a c } } { 2 a }$ 
B)  $x = \frac { - b \pm \sqrt { b ^ { 2 } - 4 a c } } { 2 a }$ 
C)  $x = \frac { \pm b \sqrt { b ^ { 2 } - 4 a c } } { 2 a }$ 
D)  $x = \frac { b \pm \sqrt { b ^ { 2 } - 4 a c } } { 2 a }$ 
A)  $x = - b \pm \frac { \sqrt { b ^ { 2 } - 4 a c } } { 2 a }$ 
B)  $x = \frac { - b \pm \sqrt { b ^ { 2 } - 4 a c } } { 2 a }$ 
C)  $x = \frac { \pm b \sqrt { b ^ { 2 } - 4 a c } } { 2 a }$ 
D)  $x = \frac { b \pm \sqrt { b ^ { 2 } - 4 a c } } { 2 a }$

Question 2

Graph: $f ( x ) = \frac { 5 } { 6 } ( x - 3 ) ^ { 2 } + 1$

Accepted Answer

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

Question 3

Solve the equation. $5 x ^ { 2 } = 2 x - 1$

Accepted Answer

The answer of Solve the equation. \(5 x ^ {...

Question 4

The solutions of the related quadratic equation are the _________ numbers of the quadratic inequality.

Accepted Answer

The answer of The solutions of the related quadratic equation...

Question 5

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

Accepted Answer

The answer of Use the quadratic formula to solve the...

Question 6

To complete the square on $x ^ { 2 } + 12 x$ , add the square of ________ of the coefficient of x .

Accepted Answer

The answer of To complete the square on \(x ^...

Question 7

Use the square root property to solve the equation. $u ^ { 2 } - 8 = 0$

Accepted Answer

The answer of Use the square root property to solve...

Question 8

Solve $2 x ^ { 2 } - 9 = 0$ by the square root property.

Accepted Answer

A)  $\left\{ \frac { 9 } { 2 } \right\}$ 
B)  $\{ \pm 3 \}$ 
C)  $\left\{ \pm \frac { 3 \sqrt { 2 } } { 2 } \right\}$ 
D)  $\{ - 3 \}$ 
A)  $\left\{ \frac { 9 } { 2 } \right\}$ 
B)  $\{ \pm 3 \}$ 
C)  $\left\{ \pm \frac { 3 \sqrt { 2 } } { 2 } \right\}$ 
D)  $\{ - 3 \}$

Question 9

Solve the inequality. Write the solution set in interval notation and graph it. $\log _ { 5 } 3$

Accepted Answer

The answer of Solve the inequality. Write the solution set...

Question 10

Use the square root property to solve the equation. $( x + 5 ) ^ { 2 } - 3 = 0$

Accepted Answer

The answer of Use the square root property to solve...

Question 11

Write $f ( x ) = - x ^ { 2 } - 4 x + 2$ in the form $f ( x ) = a ( x - h ) ^ { 2 } + k$.

Accepted Answer

A)  $f ( x ) = - ( x + 2 ) ^ { 2 } - 2$ 
B)  $f ( x ) = - ( x - 2 ) ^ { 2 } - 2$ 
C)  $f ( x ) = - ( x - 2 ) ^ { 2 } + 6$ 
D)  $f ( x ) = - ( x + 2 ) ^ { 2 } + 6$ 
A)  $f ( x ) = - ( x + 2 ) ^ { 2 } - 2$ 
B)  $f ( x ) = - ( x - 2 ) ^ { 2 } - 2$ 
C)  $f ( x ) = - ( x - 2 ) ^ { 2 } + 6$ 
D)  $f ( x ) = - ( x + 2 ) ^ { 2 } + 6$

Question 12

Find the x -and- y intercepts of the graph of the quadratic function. $f ( x ) = - x ^ { 2 } - 8 x - 7$, x -intercept(s): __________ y -intercept(s): __________

Accepted Answer

The answer of Find the x -and- y intercepts of...

Question 13

$\log _ { 5 } 3$ is an example of a __________ inequality in one variable.

Accepted Answer

The answer of $\log _ { 5 } 3$ is...

Question 14

Solve the inequality. Write the solution set in interval notation and graph it. $\log _ { 5 } 3$

Accepted Answer

The answer of Solve the inequality. Write the solution set...

Question 15

$x = \frac { - b \pm \sqrt { b ^ { 2 } - 4 a c } } { 2 a }$ is called the __________ formula.

Accepted Answer

The answer of \(x = \frac { - b \pm...

Question 16

$x ^ { 2 } + 6 x + 9$ is called a(n) __________ square trinomial because it factors as $( x + 3 ) ^ { 2 }$ .

Accepted Answer

The expression x^2 + 6x + 9 is called a

Question 17

Solve: $\frac { x ^ { 2 } - 2 x - 24 } { x + 7 } > 0$

Accepted Answer

A)  $( - 7 , - 4 ) \cup ( 6 , \infty )$ 
B)  $( - \infty , - 7 ) \cup ( - 4,6 )$ 
C)  $( - \infty , \infty )$ 
D)  $( - 2 , - 12 )$ 
A)  $( - 7 , - 4 ) \cup ( 6 , \infty )$ 
B)  $( - \infty , - 7 ) \cup ( - 4,6 )$ 
C)  $( - \infty , \infty )$ 
D)  $( - 2 , - 12 )$

Question 18

Solve the inequality. Write the solution set in interval notation and graph it. $\log _ { 5 } 3$

Accepted Answer

The answer of Solve the inequality. Write the solution set...

Question 19

Solve $( x + 5 ) ^ { 2 } = 80$ by square root property.

Accepted Answer

A)  $\{ - 9 \sqrt { 5 } , - \sqrt { 5 } \}$ 
B)  $\{ - 5 + 4 \sqrt { 5 } \}$ 
C)  $\{ 5 \pm 4 \sqrt { 5 } \}$ 
D)  $\{ - 5 \pm 4 \sqrt { 5 } \}$ 
A)  $\{ - 9 \sqrt { 5 } , - \sqrt { 5 } \}$ 
B)  $\{ - 5 + 4 \sqrt { 5 } \}$ 
C)  $\{ 5 \pm 4 \sqrt { 5 } \}$ 
D)  $\{ - 5 \pm 4 \sqrt { 5 } \}$

Question 20

Solve: $\frac { 8 } { x - 3 } \leq 3$

Accepted Answer

A)  $( - \infty , 3 ) \cup \left[ \frac { 17 } { 3 } , \infty \right)$ 
B)  $\left[ \frac { 17 } { 3 } , \infty \right)$ 
C)  $\left( - \infty , \frac { 17 } { 3 } \right]$ 
D)  $\left( 3 , \frac { 17 } { 3 } \right]$ 
A)  $( - \infty , 3 ) \cup \left[ \frac { 17 } { 3 } , \infty \right)$ 
B)  $\left[ \frac { 17 } { 3 } , \infty \right)$ 
C)  $\left( - \infty , \frac { 17 } { 3 } \right]$ 
D)  $\left( 3 , \frac { 17 } { 3 } \right]$

The solutions of $a x ^ { 2 } + b x + c = 0$ $( a \neq 0 )$ are

Graph: $f ( x ) = \frac { 5 } { 6 } ( x - 3 ) ^ { 2 } + 1$

Solve the equation. $5 x ^ { 2 } = 2 x - 1$

The solutions of the related quadratic equation are the _________ numbers of the quadratic inequality.

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

To complete the square on $x ^ { 2 } + 12 x$ , add the square of ________ of the coefficient of x .

Use the square root property to solve the equation. $u ^ { 2 } - 8 = 0$

Solve $2 x ^ { 2 } - 9 = 0$ by the square root property.

Solve the inequality. Write the solution set in interval notation and graph it. $\log _ { 5 } 3$

Use the square root property to solve the equation. $( x + 5 ) ^ { 2 } - 3 = 0$

Write $f ( x ) = - x ^ { 2 } - 4 x + 2$ in the form $f ( x ) = a ( x - h ) ^ { 2 } + k$ .

Find the x -and- y intercepts of the graph of the quadratic function. $f ( x ) = - x ^ { 2 } - 8 x - 7$ , x -intercept(s): y -intercept(s):

$\log _ { 5 } 3$ is an example of a __________ inequality in one variable.

Solve the inequality. Write the solution set in interval notation and graph it. $\log _ { 5 } 3$

$x = \frac { - b \pm \sqrt { b ^ { 2 } - 4 a c } } { 2 a }$ is called the __________ formula.

$x ^ { 2 } + 6 x + 9$ is called a(n) __________ square trinomial because it factors as $( x + 3 ) ^ { 2 }$ .

Solve: $\frac { x ^ { 2 } - 2 x - 24 } { x + 7 } > 0$

Solve the inequality. Write the solution set in interval notation and graph it. $\log _ { 5 } 3$

Solve $( x + 5 ) ^ { 2 } = 80$ by square root property.

Solve: $\frac { 8 } { x - 3 } \leq 3$

A Review of Basic Algebra

Graphs, Equations of Lines, and Functions

Systems of Equations

Inequalities

Exponents, Polynomials, and Polynomial Functions

Rational Expression and Equations

Radical Expressions and Equations

Exponential and Logarithmic Functions

Conic Sections; More Graphing

Miscellaneous Topics

Filters

Exam 8: Quadratic Equations, Functions, and Inequalities

The solutions of ax2+bx+c=0a x ^ { 2 } + b x + c = 0ax2+bx+c=0 (a≠0)( a \neq 0 )(a=0) are

Graph: f(x)=56(x−3)2+1f ( x ) = \frac { 5 } { 6 } ( x - 3 ) ^ { 2 } + 1f(x)=65​(x−3)2+1

Solve the equation. 5x2=2x−15 x ^ { 2 } = 2 x - 15x2=2x−1

The solutions of the related quadratic equation are the _________ numbers of the quadratic inequality.

Use the quadratic formula to solve the equation. 9z2+9z+2=09 z ^ { 2 } + 9 z + 2 = 09z2+9z+2=0

To complete the square on x2+12xx ^ { 2 } + 12 xx2+12x , add the square of ________ of the coefficient of x .

Use the square root property to solve the equation. u2−8=0u ^ { 2 } - 8 = 0u2−8=0

Solve 2x2−9=02 x ^ { 2 } - 9 = 02x2−9=0 by the square root property.

Solve the inequality. Write the solution set in interval notation and graph it. log⁡53\log _ { 5 } 3log5​3

Use the square root property to solve the equation. (x+5)2−3=0( x + 5 ) ^ { 2 } - 3 = 0(x+5)2−3=0

Write f(x)=−x2−4x+2f ( x ) = - x ^ { 2 } - 4 x + 2f(x)=−x2−4x+2 in the form f(x)=a(x−h)2+kf ( x ) = a ( x - h ) ^ { 2 } + kf(x)=a(x−h)2+k .

Find the x -and- y intercepts of the graph of the quadratic function. f(x)=−x2−8x−7f ( x ) = - x ^ { 2 } - 8 x - 7f(x)=−x2−8x−7 , x -intercept(s): __________ y -intercept(s): __________

log⁡53\log _ { 5 } 3log5​3 is an example of a __________ inequality in one variable.

Solve the inequality. Write the solution set in interval notation and graph it. log⁡53\log _ { 5 } 3log5​3

x=−b±b2−4ac2ax = \frac { - b \pm \sqrt { b ^ { 2 } - 4 a c } } { 2 a }x=2a−b±b2−4ac​​ is called the __________ formula.

x2+6x+9x ^ { 2 } + 6 x + 9x2+6x+9 is called a(n) __________ square trinomial because it factors as (x+3)2( x + 3 ) ^ { 2 }(x+3)2 .

Solve: x2−2x−24x+7>0\frac { x ^ { 2 } - 2 x - 24 } { x + 7 } > 0x+7x2−2x−24​>0

Solve the inequality. Write the solution set in interval notation and graph it. log⁡53\log _ { 5 } 3log5​3

Solve (x+5)2=80( x + 5 ) ^ { 2 } = 80(x+5)2=80 by square root property.

Solve: 8x−3≤3\frac { 8 } { x - 3 } \leq 3x−38​≤3

A Review of Basic Algebra

Graphs, Equations of Lines, and Functions

Systems of Equations

Inequalities

Exponents, Polynomials, and Polynomial Functions

Rational Expression and Equations

Radical Expressions and Equations

Exponential and Logarithmic Functions

Conic Sections; More Graphing

Miscellaneous Topics

Filters

The solutions of $a x ^ { 2 } + b x + c = 0$ $( a \neq 0 )$ are

Graph: $f ( x ) = \frac { 5 } { 6 } ( x - 3 ) ^ { 2 } + 1$

Solve the equation. $5 x ^ { 2 } = 2 x - 1$

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

To complete the square on $x ^ { 2 } + 12 x$ , add the square of ________ of the coefficient of x .

Use the square root property to solve the equation. $u ^ { 2 } - 8 = 0$

Solve $2 x ^ { 2 } - 9 = 0$ by the square root property.

Solve the inequality. Write the solution set in interval notation and graph it. $\log _ { 5 } 3$

Use the square root property to solve the equation. $( x + 5 ) ^ { 2 } - 3 = 0$

Write $f ( x ) = - x ^ { 2 } - 4 x + 2$ in the form $f ( x ) = a ( x - h ) ^ { 2 } + k$ .

Find the x -and- y intercepts of the graph of the quadratic function. $f ( x ) = - x ^ { 2 } - 8 x - 7$ , x -intercept(s): y -intercept(s):

$\log _ { 5 } 3$ is an example of a __________ inequality in one variable.

Solve the inequality. Write the solution set in interval notation and graph it. $\log _ { 5 } 3$

$x = \frac { - b \pm \sqrt { b ^ { 2 } - 4 a c } } { 2 a }$ is called the __________ formula.

$x ^ { 2 } + 6 x + 9$ is called a(n) __________ square trinomial because it factors as $( x + 3 ) ^ { 2 }$ .

Solve: $\frac { x ^ { 2 } - 2 x - 24 } { x + 7 } > 0$

Solve the inequality. Write the solution set in interval notation and graph it. $\log _ { 5 } 3$

Solve $( x + 5 ) ^ { 2 } = 80$ by square root property.

Solve: $\frac { 8 } { x - 3 } \leq 3$