Questions and Answers
What is the vertex form of a quadratic equation?
y = a(x - h)^2 + k
How do you find the vertex of a quadratic equation represented by the standard form?
-b/2a
What is the compound interest formula?
A = P(1 + r/n)^(nt)
What is the formula for continuous compound interest?
Signup and view all the answers
What is the half-life formula?
Signup and view all the answers
What is the discriminant formula?
Signup and view all the answers
What is the quadratic formula?
Signup and view all the answers
What is the slope formula?
Signup and view all the answers
What is the slope-intercept form of a linear equation?
Signup and view all the answers
What is the point-slope form of a linear equation?
Signup and view all the answers
What is the formula for calculating the distance between two points?
Signup and view all the answers
What is the midpoint formula?
Signup and view all the answers
What are inverses in mathematics?
Signup and view all the answers
What is an imaginary number?
Signup and view all the answers
What defines exponential growth?
Signup and view all the answers
What defines exponential decay?
Signup and view all the answers
What is the linear regression equation?
Signup and view all the answers
What is an asymptote?
Signup and view all the answers
What is the elimination method in systems of equations?
Signup and view all the answers
Study Notes
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.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Test your knowledge with these flashcards focused on important formulas for the Honors Algebra 2 final. This quiz covers key concepts such as vertex form, compound interest, and half-life formulas. Perfect for revision and reinforcing your understanding before the exam.