Advanced Algebra S1 Final Review (Ch1-Ch3)

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 and B are not both zero.

Front

How do you determine if a point lies on a line represented by an equation?

Back

To determine if a point (x, y) lies on a line, substitute the x-value into the equation and see if the resulting y-value matches the y-coordinate of the point.

Front

What is a system of linear inequalities?

Back

A system of linear inequalities consists of two or more inequalities that involve the same variables. The solution is the region where the graphs of the inequalities overlap.

Front

How do you find the slope of a line given two points?

Back

The slope (m) of a line through points (x1, y1) and (x2, y2) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What does it mean for a function to be quadratic?

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

Front

How do you find the vertex of a quadratic function?

Back

The vertex of a quadratic function in standard form f(x) = ax^2 + bx + c can be found using the formula x = -b/(2a). Substitute this x-value back into the function to find the y-coordinate.

Front

What is the difference between a function and a relation?

Back

A function is a specific type of relation where each input (x-value) is associated with exactly one output (y-value).

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) in the equation y = mx + b.

Front

How do you solve a system of equations using substitution?

Back

To solve a system of equations using substitution, solve one equation for one variable and substitute that expression into the other equation.

Front

What is the graphical representation of the equation 3x + 2y = 12?

Back

To graph the equation 3x + 2y = 12, find the x-intercept (when y=0) and the y-intercept (when x=0), then draw a line through these points.