1. UNIT 1 Intro to Algebra II

2. 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.

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

4. 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.

5. 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

6. 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

7. 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.

8. 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”.

9. Complex Numbers!

10. UNIT 2 Quadratic Functions

11. Properties of Quadratics

12. 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.

13. 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

14. The Quadratic Formula NOTES

15. Quadratic Transformations

19. UNIT 3 Exponential & Logarithmic Functions

20. Exponential Functions

22. Exponentials Functions

23. 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.

24. Continuous Growth/Decay

25. Compound Interest

26. Properties of Logarithms

27. UNIT 4 Regression Analysis

28. 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.

29. UNIT 5 Polynomial Functions

30. Factoring Polynomials

32. UNIT 6 Radicals, Absolute Value, & Circles

33. 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.

35. UNIT 7 Rational Functions

36. 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

37. 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.

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

39. 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.

40. 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

41. INVERSE VARIATION!!!

42. DIRECT VARIATION

43. Transformations!!!