Linear functions
What form is y = mx + b?
Slope-intercept form
How do you explain if a function is exponential?
An exponential function is characterized by having the variable in the exponent, while the base is a constant. Specifically, it's represented as f(x) = b^x, where 'b' is a constant and 'x' is the variable. This means the function's growth (or decay) is proportional to its value, leading to rapid changes in output as the input changes.
What are the 3 quadratic functions?
Standard Form
Factored Form
Vertex Form
What is the definition of exponents in math?
In mathematics, an exponent indicates how many times a base number should be multiplied by itself
What are the steps to solving a system of equations?
Write both equations in standard form.
Make the coefficients of one variable opposites.
Add the equations resulting from Step 2 to eliminate one variable.
Solve for the remaining variable.
Substitute the solution from Step 4 into one of the original equations.
Write the solution as an ordered pair.
What form is y - y₁ = m(x - x₁)?
Point-Slope form
What is the equation for the exponential function?
The general equation for an exponential function is f(x) = a * bˣ, where 'a' is a constant (the initial value or y-intercept), 'b' is the base (must be positive and not equal to 1), and 'x' is the exponent.
How do I solve a quadratic function?
First, we bring the equation to the form ax²+bx+c=0, where a, b, and c are coefficients. Then, we plug these coefficients in the formula: (-b±√(b²-4ac))/(2a)
What is an example of an exponent?
in 2³, the base is 2 and the exponent is 3, meaning 2 is multiplied by itself three times (2 * 2 * 2 = 8).
What are the 3 methods of solving systems of equations?
The three primary methods for solving systems of linear equations are substitution, elimination, and graphing
What form is Ax + By = C?
Standard Form
types of exponential functions
exponential growth and exponential decay.
What are the 4 types of quadratic functions?
standard form, vertex form, and intercept form
What is 4 and exponent 2?
4^2 = 4 × 4 = 16.
How to solve a system of equations algebraically in Algebra 2?
The systems are solved by solving for one variable in one of the equations, then substituting that equation into the second equation
Definition of y = 2x + 3
This equation represents a line with a slope of 2 (meaning for every 1 unit increase in x, y increases by 2) and a y-intercept of 3 (the point where the line crosses the y-axis).
What is the rule for exponential function?
An exponential function is defined by the formula f(x) = ax, where the input variable x occurs as an exponent.
What are the 3 steps of quadratic formula?
Step 1: Identify a, b, and c in the quadratic equation a x 2 + b x + c = 0 .
Step 2: Substitute the values from step 1 into the quadratic formula x = − b ± b 2 − 4 a c 2 a .
Step 3: Simplify, making sure to follow the order of operations
What are the 7 rules of exponents?
product rule, quotient rule, power rule, zero exponent rule, negative exponent rule, power of a product rule, and power of a quotient rule
What are the 4 methods of solving simultaneous equations?
The methods include graphical, substitution, Guass-Jordan elimination and determinants
Definition of f(x) = -0.5x + 5
This is equivalent to the slope-intercept form but uses function notation, where f(x) represents the y-value for a given x-value. In this example, the slope is -0.5, and the y-intercept is 5.
What is a in the exponential function?
In an exponential function, the variable a represents the initial value or the starting point of the function. It's the y-intercept of the function's graph when x=0.
How to factor a quadratic formula?
first solve the quadratic equation using the formula to find its roots, then express the equation in factored form using those roots
What is 72 in the rule of 72?
In the Rule of 72, the number 72 is used as the numerator in a simple calculation to estimate how long it will take for an investment to double at a given annual interest rate. Specifically, you divide 72 by the annual interest rate to get an approximation of the number of years it will take for your investment to double.
What are the 3 types of solutions to a system of equations?
The most common method for solving simultaneous equations is the elimination method which means one of the unknowns will be removed from each equation.