Honors Algebra 2 Final: Important Formulas

Important Algebra 2 Formulas

Vertex Form
Represents a quadratic function, expressed as ( y = a(x-h)^2 + k ), where ((h,k)) is the vertex of the parabola.
Finding the Vertex
The x-coordinate of the vertex can be determined using the formula ( -\frac{b}{2a} ).
Compound Interest Formula
Used to calculate the amount ( A ) after a certain period with compounded interest, given by ( A = P(1 + \frac{r}{n})^{nt} ).
Continuous Compound Interest
For continuous growth, the amount is calculated with the formula ( A = Pe^{rt} ), where ( e ) is Euler's number.
Half Life Formula
Models the decay of substances, defined by ( y = C \left( \frac{1}{2} \right)^{\frac{t}{h}} ); ( C ) is the initial amount, ( t ) is time, and ( h ) is the half-life.
Discriminant Formula
Used to determine the nature of the roots of a quadratic equation, calculated as ( b^2 - 4ac ).
Quadratic Formula
Provides solutions for quadratic equations in standard form: ( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ).
Slope Formula
Calculates the slope between two points, defined as ( \frac{y_2 - y_1}{x_2 - x_1} ).
Slope-Intercept Form
A linear equation format where ( y = mx + b ); ( m ) is the slope and ( b ) is the y-intercept.
Point-Slope Form
Represents a linear equation based on a point ((x_1, y_1)) and slope ( m), formulated as ( y - y_1 = m(x - x_1) ).
Distance Formula
Calculates the distance ( d ) between two points ((x_1, y_1)) and ((x_2, y_2)), given by ( d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2} ).
Midpoint Formula
Finds the midpoint of a segment between two points, expressed as ( \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) ).
Inverses
Functions that, when applied consecutively, return to the original value; they "reverse" each other.
Imaginary Number
Defined as the square root of (-1), represented as ( i ).
Exponential Growth
Characterized by a base of 1 or more, leading to an increase in values.
Exponential Decay
Features a base between 0 and 1, resulting in a decrease in values over time.
Linear Regression Equation
Represents the equation for the line of best fit used in statistical analysis to model relationships between variables.
Asymptote
A line that a graph approaches indefinitely but never intersects.
Systems of Equations - Elimination Method
A technique to solve systems of equations by adding or subtracting equations to eliminate one variable.