UNIT 1 Intro to Algebra II

NOTES Like Terms: terms in an algebraic expression or equation whose variable AND exponents are the same When we combine Like Terms by addition or subtraction, we DO NOT change the variable or its exponent, just the coefficient out front.

NOTES When we multiply terms in a polynomial expression: Multiply the leading coefficients. Add the exponents of like bases.

Factoring Perfect Square Quadratics Perfect square trinomial: a polynomial expression whose two factors are identical Difference of squares: two terms that are squared and separated by a subtraction sign. The two factors are identical except they have a different sign.

Factoring Perfect Square Quadratics Greatest Common Factor: in a set of algebraic terms, it is the highest number and lowest power shared by the terms

Linear Functions!!! Linear functions are straight lines. Slope-intercept form of a linear function is y = mx + b WHERE m = slope b = y-intercept (x, y) = points on the graph

Inverse Function INVERSE FUNCTION: a function obtained by expressing the dependent variable of one function as the independent variable of another. The BIG IDEA of inverse functions is that they undo each other. Graphically, the inverse function is a function reflected over the line y = x.

Inverse Function To find the inverse of a function: 1. Switch “x” and “y”. 2. Solve the equation for “y”. 3. Substitute f -1 (x) in for “y”.

Complex Numbers!

UNIT 2 Quadratic Functions

Properties of Quadratics

The Axis of Symmetry is the line that cuts a quadratic function directly in half. The Axis of Symmetry is the vertical line that runs through the “x” coordinate of the vertex.

Properties of Quadratics We can find the x-intercepts of a quadratic function 3 ways: 1.Using the quadratic formula: 2. By factoring 3. By using the “2 nd trace” button and “zero” button on our calculator

The Quadratic Formula NOTES

Quadratic Transformations

UNIT 3 Exponential & Logarithmic Functions

Exponential Functions

Exponentials Functions

Graphing Exponentials! We can find the y-intercept by plugging in “0” for “x” We can find x-intercepts by plugging in “o” for “y” and solving for “x” OR using our calculator! End behavior describes how a function behaves as “x” values get really big and really small.

Continuous Growth/Decay

Compound Interest

Properties of Logarithms

UNIT 4 Regression Analysis

Regression Analysis - Notes 1.Make one variable “x” and one “y”. 2.Hit “Stat”, then “Edit”. Put your “x” values in L1. Put your “y” values in L2. 3.Make sure you turn on Stat Plot and hit “Zoom”, then “9” to see your data. 4.Decide if the data is linear, quadratic, or exponential. 5.Find the line of best fit by hitting “Stat”, then “Calc”, then the type of function (LinReg, QuadReg, or ExpReg) 6.Answer the question being asked using your knowledge of the function.

UNIT 5 Polynomial Functions

Factoring Polynomials

UNIT 6 Radicals, Absolute Value, & Circles

Rational Exponent Properties 1.When we multiply like bases, ADD exponents. 2.When we divide like bases, SUBTRACT exponents. 3.When we raise an exponent to another exponent, distribute the exponent. 4.You can change the sign of an exponent by flipping its place in the fraction.

UNIT 7 Rational Functions

Rational Functions!!! RATIONAL FUNCTION: A function which can be written as a fraction with 2 polynomial functions. Rules for simplifying/multiplying polynomials: 1.Multiply (if possible) 2.Take out a GCF (if possible) 3.Factor (if possible) 4.Cancel out where possible 5.Use exponent rules to reduce

Graphing Rational Functions Vertical Asymptote: a vertical line that a rational function approaches but can never actually cross Expressed as x = “?” lines We find vertical asymptotes by finding the values where the denominator of a rational function equals ZERO.

Graphing Rational Functions Horizontal Asymptote: a horizontal line that a rational function approaches but can never actually cross Expressed as y = “?” lines

Finding Horizontal Asymptotes 1.If the numerator has a lower highest power then the denominator, the HA is at the line y = 0. 2.If the numerator and the denominator have the same highest power, divide the leading coefficients to find the HA. 3.If the numerator has a higher highest power than the denominator, then the function has no horizontal asymptote.

X and Y-Intercepts!!! To find the y-intercept, plug in “0” for “x”. To find the x-intercept, set the numerator of the fraction equal to “0” and

INVERSE VARIATION!!!

DIRECT VARIATION

Transformations!!!