24-25 Final Review #11

Front

What is the definition of an absolute value equation?

Back

An absolute value equation is an equation that contains an absolute value expression, which represents the distance of a number from zero on the number line.

Front

How do you solve an absolute value equation like |x - 3| = 6?

Back

To solve |x - 3| = 6, set up two equations: x - 3 = 6 and x - 3 = -6. Solve each equation to find x = 9 and x = -3.

Front

What does it mean for a variable to be independent in an equation?

Back

An independent variable is a variable that represents a quantity that is being manipulated or changed in an experiment or equation, often denoted as x.

Front

What does it mean for a variable to be dependent in an equation?

Back

A dependent variable is a variable that represents a quantity that depends on the value of the independent variable, often denoted as y.

Front

How do you evaluate a function at a specific point, such as h(-6) for h(x) = -2x^2 - 3x + 4?

Back

To evaluate h(-6), substitute -6 for x in the function: h(-6) = -2(-6)^2 - 3(-6) + 4 = -50.

Front

What is the formula for finding the slope of a line given two points (x1, y1) and (x2, y2)?

Back

The slope m is calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, indicating that there is no vertical change as you move along the line.

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

How do you convert a word problem into an algebraic equation?

Back

Identify the variables, translate the words into mathematical operations, and set up the equation based on the relationships described.

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex of a quadratic function is the highest or lowest point on the graph, representing the maximum or minimum value of the function.