Algebra Formulas Quiz

Algebra Formulas

• Slope: Calculated using the formula ( m = \frac{y_2 - y_1}{x_2 - x_1} ); represents the steepness of a line.

• Slope-Intercept Form: Expressed as ( y = mx + b ), where ( m ) is the slope and ( b ) is the y-intercept, indicating the point where the line crosses the y-axis.

• Circle Equation: Represents a circle in a coordinate plane as ( (x - h)^2 + (y - k)^2 = r^2 ); ( (h, k) ) is the center, and ( r ) is the radius.

• Pythagorean Theorem: Fundamental relation in Euclidean geometry, stated as ( a^2 + b^2 = c^2 ), where ( c ) is the hypotenuse of a right triangle.

• Difference of Perfect Cubes: Formula given by ( a^3 - b^3 = (a - b)(a^2 + ab + b^2) ); useful for factoring cubic expressions.

• Quadratic Formula: Used to find the roots of a quadratic equation; expressed as ( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ).

• Point-Slope Form: Written as ( y = y_1 + m(x - x_1) ); used to write the equation of a line given a point ((x_1, y_1)) and the slope ( m ).

• Distance Formula: Determines the distance between two points in a plane, defined as ( d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2} ).

• Midpoint Formula: Finds the midpoint between two points ((x_1, y_1)) and ((x_2, y_2)); calculated as ( \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right) ).

• Difference of Perfect Squares: Expressed as ( a^2 - b^2 = (a - b)(a + b) ); a key technique for factoring.

• Sum of Perfect Cubes: Given by the formula ( a^3 + b^3 = (a + b)(a^2 - ab + b^2) ); essential for simplifying expressions involving cubes.