Algebra Chapter 8

Question 1

What is the formula for the slope of a line?

Answer 1

m = (y2 - y1) / (x2 - x1)

Question 2

True or False: The slope of a line represents the rate of change.

Answer 2

True

Question 3

Fill in the blank: The equation of a linear function is typically written in the form y = mx + ____.

Answer 3

b

Question 4

What does the ‘b’ represent in the linear equation y = mx + b?

Answer 4

The y-intercept

Question 5

Identify the slope in the equation y = 3x + 4.

Answer 5

3

Question 6

What type of function is represented by a quadratic equation?

Answer 6

A polynomial function of degree 2

Question 7

True or False: The standard form of a quadratic equation is ax^2 + bx + c = 0.

Answer 7

True

Question 8

Fill in the blank: The vertex of a parabola can be found using the formula x = ____.

Answer 8

-b / (2a)

Question 9

What is the axis of symmetry in a quadratic function?

Answer 9

x = -b / (2a)

Question 10

What are the roots of a quadratic equation?

Answer 10

The values of x that make the equation equal to zero.

Question 11

Name one method to solve a quadratic equation.

Answer 11

Factoring, completing the square, or using the quadratic formula.

Question 12

What is the quadratic formula?

Answer 12

x = (-b ± √(b² - 4ac)) / (2a)

Question 13

True or False: A quadratic function can have zero, one, or two real roots.

Answer 13

True

Question 14

Fill in the blank: The discriminant is given by the expression ____.

Answer 14

b² - 4ac

Question 15

What does a positive discriminant indicate?

Answer 15

Two distinct real roots.

Question 16

What does a discriminant of zero indicate?

Answer 16

One real root (a repeated root).

Question 17

What does a negative discriminant indicate?

Answer 17

No real roots (two complex roots).

Question 18

What is the factored form of a quadratic function?

Answer 18

y = a(x - r1)(x - r2)

Question 19

Identify the vertex form of a quadratic function.

Answer 19

y = a(x - h)² + k

Question 20

What do the variables h and k represent in vertex form?

Answer 20

The coordinates of the vertex (h, k).

Question 21

True or False: A quadratic function opens upwards if a > 0.

Answer 21

True

Question 22

What is the formula for the area of a triangle?

Answer 22

Area = 1/2 * base * height

Question 23

Fill in the blank: The sum of the angles in a triangle is ____ degrees.

Answer 23

180

Question 24

What is the Pythagorean theorem?

Answer 24

a² + b² = c²

Question 25

True or False: The sides of a right triangle must satisfy the Pythagorean theorem.

Answer 25

True

Question 26

What is the formula for the circumference of a circle?

Answer 26

C = 2πr

Question 27

What is the formula for the area of a circle?

Answer 27

A = πr²

Question 28

Fill in the blank: The distance formula between two points (x1, y1) and (x2, y2) is ____.

Answer 28

√((x2 - x1)² + (y2 - y1)²)

Question 29

How do you find the midpoint between two points?

Answer 29

Midpoint = ((x1 + x2)/2, (y1 + y2)/2)

Question 30

What is the formula for the slope-intercept form of a line?

Answer 30

y = mx + b

Question 31

What does 'm' represent in the slope-intercept form?

Answer 31

The slope of the line.

Question 32

True or False: Linear equations can be represented graphically as straight lines.

Answer 32

True

Question 33

What is the formula for a direct variation?

Answer 33

y = kx, where k is a non-zero constant.

Question 34

In the equation y = kx, what does 'k' represent?

Answer 34

The constant of variation.

Question 35

What is the definition of a function?

Answer 35

A relation where each input has exactly one output.

Question 36

Fill in the blank: A function can be represented as a ____.

Answer 36

set of ordered pairs

Question 37

True or False: The vertical line test can be used to determine if a relation is a function.

Answer 37

True

Question 38

What is an asymptote?

Answer 38

A line that a graph approaches but never touches.