Algebra Review

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves. It can be found using the formula x = -b/(2a) for a quadratic equation in the form ax^2 + bx + c.

Front

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

Back

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as the x-values increase, the y-values decrease, meaning the line falls from left to right.

Front

What is the rate of change in a linear function?

Back

The rate of change is the same as the slope of the line, representing how much the dependent variable (y) changes for a unit change in the independent variable (x).

Front

What is the equation of a line in slope-intercept form?

Back

The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you find the equation of a line parallel to a given line?

Back

To find the equation of a line parallel to a given line, use the same slope as the given line and the point-slope form of the equation: y - y1 = m(x - x1).

Front

What is the relationship between parallel lines in terms of slope?

Back

Parallel lines have the same slope but different y-intercepts.

Front

How do you find the equation of a line perpendicular to a given line?

Back

To find the equation of a line perpendicular to a given line, use the negative reciprocal of the slope of the given line and the point-slope form of the equation.

Front

What is the relationship between perpendicular lines in terms of slope?

Back

Perpendicular lines have slopes that are negative reciprocals of each other, meaning if one slope is m, the other is -1/m.

Front

What is a quadratic function?

Back

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