Question 1

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 2

Find the x -intercept(s) for $f ( x ) = 3 x ^ { 2 } + 5 x - 2$ .

Accepted Answer

A)  $( - 2,0 ) , \left( \frac { 1 } { 3 } , 0 \right)$ 
B)  $\left( - \frac { 1 } { 3 } , 0 \right) , ( 2,0 )$ 
C)  $\left( - \frac { 2 } { 3 } , 0 \right) , ( - 1,0 )$ 
D)  $\left( \frac { 2 } { 3 } , 0 \right) , ( 1,0 )$ 
A)  $( - 2,0 ) , \left( \frac { 1 } { 3 } , 0 \right)$ 
B)  $\left( - \frac { 1 } { 3 } , 0 \right) , ( 2,0 )$ 
C)  $\left( - \frac { 2 } { 3 } , 0 \right) , ( - 1,0 )$ 
D)  $\left( \frac { 2 } { 3 } , 0 \right) , ( 1,0 )$

Question 3

Solve: $x ^ { 2 } - 4 x - 12 \leq 0$

Accepted Answer

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

Question 4

Evaluate the expression. $\frac { - 2 \pm \sqrt { 2 ^ { 2 } - 4 ( 1 ) ( - 8 ) } } { 2 ( 1 ) }$

Accepted Answer

The answer of Evaluate the expression. \(\frac { - 2...

Question 5

Refer to the graph.   What are the x -intercepts of the graph?
 __________ What is the y -intercept of the graph?
 __________ What is the vertex?
 __________ What is the axis of symmetry?
 x = __________ What is the domain?
 (Use interval notation.) __________ What is the range?
 (Use interval notation.) __________

Accepted Answer

The answer of Refer to the graph.   What...

Question 6

The height of a triangle is 3 meters longer than twice its base. Find the base of the triangle if the area is 76 square meters.

Accepted Answer

The answer of The height of a triangle is 3...

Question 7

Graph the inequality. $\log _ { 5 } 3$

Accepted Answer

The answer of Graph the inequality. \(\log _ { 5...

Question 8

$\frac { x - 1 } { x ^ { 2 } - x - 17 } \leq 0$ is an example of a __________ inequality in one variable.

Accepted Answer

The given inequality \frac { x - 1 } { x

Question 9

What number is added to each side of the equation $4 x ^ { 2 } + 48 x = 7$ in completing the square?

Accepted Answer

A)  75 
B)  36 
C)  4 
D)  48 
A)  75 
B)  36 
C)  4 
D)  48

Question 10

Solve the equation. $x ^ { 2 } - 2 x + 10 = 0$

Accepted Answer

The answer of Solve the equation. \(x ^ { 2...

Question 11

Solve the equation. Approximate the solutions to two decimal places. $3 x ^ { 2 } + 7 x = - 1$

Accepted Answer

The answer of Solve the equation. Approximate the solutions to...

Question 12

Write the equation in standard form. $4 x ^ { 2 } = - 4 x + 1$

Accepted Answer

The answer of Write the equation in standard form. \(4...

Question 13

Graph $f ( x ) = - x ^ { 2 } - 4 x - 3$

Accepted Answer

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

Question 14

$f ( x ) = a ( x - h ) ^ { 2 } + k$ is called the _________ form of the equation of a quadratic function.

Accepted Answer

The answer of \(f ( x ) = a (...

Question 15

Find a number between 0 and 1 such that the difference of the number and its square is a maximum.

Accepted Answer

The answer of Find a number between 0 and 1...

Question 16

What number must be added to $x ^ { 2 } + \sqrt { 7 } x$ to make a perfect-square trinomial?

Accepted Answer

The answer of What number must be added to \(x...

Question 17

The graph of $f ( x ) = 3 x ^ { 2 } + 1$ is shown below. Explain why the quadratic inequality $3 x ^ { 2 } + 1 < 0$ has no solution.

Accepted Answer

None of th

Question 18

Find the x -and y -intercepts of the graph of the quadratic function. $f ( x ) = x ^ { 2 } + 2 x + 1$ x -intercept(s): __________ y -intercept(s): __________

Accepted Answer

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

Question 19

Refer to the graph. Fill in the blank.   The vertical line x=3 divides the parabola into two halves. This line is called the __________.

Accepted Answer

The answer of Refer to the graph. Fill in the...

Question 20

Give the axis of symmetry for $f ( x ) = 8 ( x - 4 ) ^ { 2 } + 1$ .

Accepted Answer

A)  x=1 
B)  x=8 
C)  x=4 
D)  x=-4 
A)  x=1 
B)  x=8 
C)  x=4 
D)  x=-4

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

Find the x -intercept(s) for $f ( x ) = 3 x ^ { 2 } + 5 x - 2$ .

Solve: $x ^ { 2 } - 4 x - 12 \leq 0$

Evaluate the expression. $\frac { - 2 \pm \sqrt { 2 ^ { 2 } - 4 ( 1 ) ( - 8 ) } } { 2 ( 1 ) }$

Refer to the graph. What are the x -intercepts of the graph? What is the y -intercept of the graph? What is the vertex? What is the axis of symmetry? x = What is the domain? (Use interval notation.) What is the range? (Use interval notation.)

The height of a triangle is 3 meters longer than twice its base. Find the base of the triangle if the area is 76 square meters.

Graph the inequality. $\log _ { 5 } 3$

$\frac { x - 1 } { x ^ { 2 } - x - 17 } \leq 0$ is an example of a __________ inequality in one variable.

What number is added to each side of the equation $4 x ^ { 2 } + 48 x = 7$ in completing the square?

Solve the equation. $x ^ { 2 } - 2 x + 10 = 0$

Solve the equation. Approximate the solutions to two decimal places. $3 x ^ { 2 } + 7 x = - 1$

Write the equation in standard form. $4 x ^ { 2 } = - 4 x + 1$

Graph $f ( x ) = - x ^ { 2 } - 4 x - 3$

$f ( x ) = a ( x - h ) ^ { 2 } + k$ is called the _________ form of the equation of a quadratic function.

Find a number between 0 and 1 such that the difference of the number and its square is a maximum.

What number must be added to $x ^ { 2 } + \sqrt { 7 } x$ to make a perfect-square trinomial?

The graph of $f ( x ) = 3 x ^ { 2 } + 1$ is shown below. Explain why the quadratic inequality $3 x ^ { 2 } + 1 < 0$ has no solution. $The graph of f ( x ) = 3 x ^ { 2 } + 1 is shown below. Explain why the quadratic inequality 3 x ^ { 2 } + 1 < 0 has no solution.$

Find the x -and y -intercepts of the graph of the quadratic function. $f ( x ) = x ^ { 2 } + 2 x + 1$ x -intercept(s): y -intercept(s):

Refer to the graph. Fill in the blank. The vertical line x=3 divides the parabola into two halves. This line is called the __________.

Give the axis of symmetry for $f ( x ) = 8 ( x - 4 ) ^ { 2 } + 1$ .

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

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

Find the x -intercept(s) for f(x)=3x2+5x−2f ( x ) = 3 x ^ { 2 } + 5 x - 2f(x)=3x2+5x−2 .

Solve: x2−4x−12≤0x ^ { 2 } - 4 x - 12 \leq 0x2−4x−12≤0

Evaluate the expression. −2±22−4(1)(−8)2(1)\frac { - 2 \pm \sqrt { 2 ^ { 2 } - 4 ( 1 ) ( - 8 ) } } { 2 ( 1 ) }2(1)−2±22−4(1)(−8)​​

The height of a triangle is 3 meters longer than twice its base. Find the base of the triangle if the area is 76 square meters.

Graph the inequality. log⁡53\log _ { 5 } 3log5​3

x−1x2−x−17≤0\frac { x - 1 } { x ^ { 2 } - x - 17 } \leq 0x2−x−17x−1​≤0 is an example of a __________ inequality in one variable.

What number is added to each side of the equation 4x2+48x=74 x ^ { 2 } + 48 x = 74x2+48x=7 in completing the square?

Solve the equation. x2−2x+10=0x ^ { 2 } - 2 x + 10 = 0x2−2x+10=0

Solve the equation. Approximate the solutions to two decimal places. 3x2+7x=−13 x ^ { 2 } + 7 x = - 13x2+7x=−1

Write the equation in standard form. 4x2=−4x+14 x ^ { 2 } = - 4 x + 14x2=−4x+1

Graph f(x)=−x2−4x−3f ( x ) = - x ^ { 2 } - 4 x - 3f(x)=−x2−4x−3

f(x)=a(x−h)2+kf ( x ) = a ( x - h ) ^ { 2 } + kf(x)=a(x−h)2+k is called the _________ form of the equation of a quadratic function.

Find a number between 0 and 1 such that the difference of the number and its square is a maximum.

What number must be added to x2+7xx ^ { 2 } + \sqrt { 7 } xx2+7​x to make a perfect-square trinomial?

The graph of f(x)=3x2+1f ( x ) = 3 x ^ { 2 } + 1f(x)=3x2+1 is shown below. Explain why the quadratic inequality 3x2+1<03 x ^ { 2 } + 1 < 03x2+1<0 has no solution.

Find the x -and y -intercepts of the graph of the quadratic function. f(x)=x2+2x+1f ( x ) = x ^ { 2 } + 2 x + 1f(x)=x2+2x+1 x -intercept(s): __________ y -intercept(s): __________

Refer to the graph. Fill in the blank. The vertical line x=3 divides the parabola into two halves. This line is called the __________.

Give the axis of symmetry for f(x)=8(x−4)2+1f ( x ) = 8 ( x - 4 ) ^ { 2 } + 1f(x)=8(x−4)2+1 .

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

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

Find the x -intercept(s) for $f ( x ) = 3 x ^ { 2 } + 5 x - 2$ .

Solve: $x ^ { 2 } - 4 x - 12 \leq 0$

Evaluate the expression. $\frac { - 2 \pm \sqrt { 2 ^ { 2 } - 4 ( 1 ) ( - 8 ) } } { 2 ( 1 ) }$

Graph the inequality. $\log _ { 5 } 3$

$\frac { x - 1 } { x ^ { 2 } - x - 17 } \leq 0$ is an example of a __________ inequality in one variable.

What number is added to each side of the equation $4 x ^ { 2 } + 48 x = 7$ in completing the square?

Solve the equation. $x ^ { 2 } - 2 x + 10 = 0$

Solve the equation. Approximate the solutions to two decimal places. $3 x ^ { 2 } + 7 x = - 1$

Write the equation in standard form. $4 x ^ { 2 } = - 4 x + 1$

Graph $f ( x ) = - x ^ { 2 } - 4 x - 3$

$f ( x ) = a ( x - h ) ^ { 2 } + k$ is called the _________ form of the equation of a quadratic function.

What number must be added to $x ^ { 2 } + \sqrt { 7 } x$ to make a perfect-square trinomial?

The graph of $f ( x ) = 3 x ^ { 2 } + 1$ is shown below. Explain why the quadratic inequality $3 x ^ { 2 } + 1 < 0$ has no solution. $The graph of f ( x ) = 3 x ^ { 2 } + 1 is shown below. Explain why the quadratic inequality 3 x ^ { 2 } + 1 < 0 has no solution.$

Find the x -and y -intercepts of the graph of the quadratic function. $f ( x ) = x ^ { 2 } + 2 x + 1$ x -intercept(s): y -intercept(s):

Give the axis of symmetry for $f ( x ) = 8 ( x - 4 ) ^ { 2 } + 1$ .