Algebra 2

 

Algebra 2 Course Outline
Algebra 2 Notes, Assignments, and Video Links

2017-2018 Calendar (semester-at-a-glance) for Algebra 2 (dates subject to change)

Algebra 2 First Semester Assignments (dates subject to change)

Algebra 2 Second Semester Assignments (dates subject to change)

 

filled in notes worksheets video links
1.1 notes 1.1 worksheet

Solving word problems with a linear equation in one variable

Several examples of setting up and solving word problems

another example of solving a word problem and then the equation

solving and checking your answer

1.2 notes 1.2 worksheet

 graphing a linear equation

converting standard form to slope intercept form and graphing using intercepts

review of slope, graphing, and equations of lines in several forms

graphing lines by finding intercepts

1.3 notes 1.3 worksheet

 transformations of linear functions

horizontal and vertical shifts (translations up or down)

more transformations of linear functions

even more transformations of linear functions

1.4 notes 1.4 worksheet

example of solving a system by graphing

solving a system by graphing and the 3 kinds of systems we see

several examples of solving a system by graphing-- lots of good conversation!

two more examples of graphing to solve a system of linear equations

1.5 notes 1.5 worksheet

solving systems of equations by substitution

solving linear systems by substitution

substitution method for solving a system of linear equations

solving systems of equations by elimination

solving linear systems by elimination and a word problem

solving linear systems by elimination

  ACT practice worksheet  
 

systems picture puzzle practice

systems picture puzzle answer sheet

 
1.6 notes 1.6 worksheet

intro to solving a system of 3 equations in 3 variables

solving a system of equations with 3 variables

another example of solving a sytem of 3 equations in 3 variables

another system of 3 equations in 3 variables

yet another example of solving a 3x3 system

  1.6 second worksheet (#2)  
  review of algebra 1 inequalities worksheet (for after the test)

graphing linear inequalities in two variables

more examples of graphing linear inequalities in two variables

even more examples of graphing linear inequalities in two variables

solving inequalities, graphing them, and interval notation

1.7 notes 1.7 worksheet

solving compound inequalities

solving and graphing compound inequalities

more compound inequalities

inequalities with and statements

more inequalities with and statements

inequalities with or statements

1.8 notes 1.8 worksheet

lots of examples of absolute value equations and inequalities

solving absolute value equations and inequalities

solving absolute value equations

more on solving absolute value equations

solving absolute value inequalities

solving absolute value inequalities, graphing, and interval notation

1.9 notes 1.9 worksheet

graphing absolute value functions with transformations

more examples of graphing absolute value functions

more transformations of absolute value functions

graphing absolute value functions with a table

1.10 notes 1.10 worksheet

graphing piecewise-defined functions

examples of graphing piecewise functions (ignore the 3rd example)

another example of a piecewise function

example of a step function

another step function

one more step function

1.11 notes 1.11 worksheet

graphing a system of linear inequalities in two variables

more examples of graphing a system of linear inequalities

even more examples of systems of linear inequalities in two variables

  review worksheet of 1.7-1.11  
2.1 notes 2.1 worksheet

graphing quadratic functions in standard form

more on graphing quadratic functions, vertex, axis of symmetry, opening up or down, and intercepts

graphing using a table and finding the vertex

characteristics of quadratic functions

more examples of finding key characteristics of quadratic functions

another video on key characteristics of quadratic functions

2.2 notes 2.2 worksheet

using transformations to graph quadratic functions

graphing quadratic functions by transformations

more graphing by transformations and tables

Ms. Harris at FHC talking about transformations of parabolas

graphing quadratic functions given in vertex form

several examples of transformations of parabolas

2.3 notes 2.3 worksheet

converting from standard form to vertex form

another example of standard form to vertex form

another standard form to vertex form example

more examples of going from standard from to vertex form including how to handle fractions

converting from vertex form to standard form

changing from vertex form to standard form

  radical review worksheet

simplifying radicals with a prime factor tree

simplifying radicals when you know squares

multiplying and dividing radical expressions

multiplying and dividing radicals

rationalizing the denominator

several examples of rationalizing the denominator

2.4 notes

2.4 worksheet

second 2.4 worksheet (day 2, after the quiz over graphing parabolas and quadratic functions)

introduction to imaginary numbers

square roots of negative numbers

more square roots of negative numbers

several examples of square roots of negative numbers

adding and subtracting complex numbers

add and subtract complex numbers

multiplying and dividing complex numbers

squaring a complex number

multiply and divide complex numbers

getting the i out of the denominator

rationalizing the denominator using a complex conjugate

add, subtract, multiply, and divide complex numbers

2.5 notes 2.5 worksheet

solve quadratic equations by the square root method

more examples of using square root of each side of an equation to solve an equation

lots of examples of various types that are all solved by the square root method

solve quadratic equations by completing the square

lots of examples of solving by completing the square

completing the square when the first coefficient is not 1 (when there is a number in front of x2)

2.6 notes 2.6 worksheet

solve quadratic equations by factoring

several examples of solving quadratic equations by factoring

example of solving a quadratic equation by factoring using guess and check to factor

a few examples of solving a quadratic equation by factoring using guess and check and by using the ac method (also called the" product sum" or "big x" method)

2.7 notes 2.7 worksheet

solve quadratic equations using the quadratic formula

several examples of solving quadratic equations using the quadratic formula

a few more examples of using the quadratic formula to solve equations

using the discriminant to determine the kinds of solutions and then going on to find those solutions by using the quadratic formula

several examples of using the discriminant to determine the nature of the solution(s) of a quadratic equation

explanation of the discriminant and the nature of roots of a quadratic

using the discriminant to figure out what kinds of roots a quadratic equation will have and also looking at what the graph will look like

2.8 notes 2.8 worksheet

general function for height and time for any object thrown (explanation of that h(t)= -16t2 + v0t + h0 formula) with a word problem example

ball thrown in the air

more projectile problems with explanation of each of the numbers in the equation

height of a ball problem

when does a ball hit the ground problem

sidewalk around a pool problem

cost and profit problem

word problem looking for a minimum

finding lowest depth a diver reaches and when he comes back to the surface of the pool

profit word problem

more word problems

volume of a box word problem

3.1 notes 3.1 worksheet

add, subtract, and multiply polynomials

more examples of adding, subtracting, and multiplying polynomials

3.2 notes 3.2 worksheet

polynomial long division- several examples

polynomial long division

two examples of polynomial long division

another example of polynomial long division

synthetic division

another example of synthetic division

synthetic division explanation

using synthetic division to evaluate a function at a certain number (also called "synthetic substitution"), including a quick explanation of WHY it works

another example of synthetic substituion, using synthetic division to find the value of a function at some number

3.3 notes 3.3 worksheet

factoring polynomials example

several examples of factoring polynomials

more examples of factoring

focus on just the sum of cubes and difference of cubes

3.4 notes 3.4 worksheet

use the Factor Theorem to determine whether
linear binomials are factors of polynomials

two ways to show that a binomial is a factor of a polynomial

checking whether a binomail is a factor (or not) of a polynomial and also using a given factor of a polynomial to find the other factors

factoring a polynomial when one factor is given to you

when given one factor of a polynomial, find all the other factors (she uses long division, but we could use synthetic division instead)

given two factors of a polynomial, use synthetic division to find the other factors

3.5 notes 3.5 worksheet

how to find the degree of a monomial and of a polynomial

finding the degree of a polynomial

Determining the number of real zeros and the number of turning points from the degree

what degree tells us about the number of x-intercepts and turning points

x-intercepts and turning points, and how they relate to degree

end behavior of polynomials

another set of examples of end behavior

describing end behavior of functions

Finding the zeros and multiplicity of polynomials

Find multiplicity and use it to graph a polynomial

Using multiplicity to graph polynomials

nice summary of end behavior, finding zeros, and multiplicity

3.6 notes 3.6 worksheet

wow! NINE examples of factoring to find the roots (also called zeros or x-intercepts) of a polynomial and discussion of the multiplicity of the roots

factoring and finding the zeros of a polynomial

factoring polynomials and finding multiplicity of roots (includes one example with irrational roots)

a couple examples of factoring 4th degree polynomials and finding the roots (includes some irrational roots)

one example of using factoring to find roots (includes roots that are irrational)

sketching a polynomial function after it has been factored

four examples of sketching polynomials using end behavior and multiplicity

several more examples of sketching polynomials

nice overview of 3.5 and 3.6 work with a couple examples

using the rational root theorem, long division, and factoring to find the real roots of a polynomial (there would be 2 imaginary or complex roots, as well, but she doesn't show those here)

using the rational root theorem (ps and qs)to find all the factors of a polynomial

using the rational zero theorem (ps and qs) to find all the roots of a polynomial

finding all the roots of a polynomial via the rational root theorem (ps and qs) and synthetic division

using the rational root theorem (ps and qs) to find possible rational roots and then finding the remaining roots after synthetic division

3.7 notes 3.7 worksheet

determining the possible number of positive, negative, or complex roots with Descartes' Rule of Signs

using Descartes Rule of Signs

Descartes Rule of Signs

Using Descartes' Rule of Signs

Using the rational root theorem (ps and qs) with Descartes' Rule of Signs and synthetic division to find roots of a polynomial-- started, but not finished-- she finds the first root

Descartes Rule of Signs and then finding all the roots of a polynomial and he finds the last 2 roots using completing the square

Descartes' Rule of Signs, the rational root theorem (ps and qs), synthetic division, factoring, and square root method to find the roots of a polynomial

Rational root theorem (ps and qs), Descartes' Rule of Signs, synthetic division, and the quadratic formula to find roots of a polynomial (includes 2 imaginary or complex solutions)

3.8 notes 3.8 worksheet

writing a polynomial if you are given some real zeros, roots, or x-intercepts

writing a polynomial when given some real roots (includes a root that is a fraction) and just leaves the resulting fractions in the answer

writing a polynomial when given some real roots, but when you don't want to deal with the fractions that you're given

writing a polynomial when you're given some real zeros or some real and some imaginary zeros

several examples of writing polynomials when you're given zeros that include irrational or complex roots

finding a polynomial equation with given roots

writing a polynomial from the zeros, including complex zeros

  3.5-3.8 mid-unit worksheet  
3.9 notes 3.9 worksheet

sketching graphs of polynomials, including the zeros (with their multiplicity), the y-intercept, and the end behavior

sketching a polynomial, including the use of the rational root theorem (ps and qs) and synthetic division

sketching a polynomial and she also finds additional points (with a chart) to help her graph the function more accurately

finding intervals where a function is increasing or decreasing (also finds where the polynomial is positive or negative)

starting with a graph, determining sign of lead coefficient and degree of a polynomial - several examples

more examples of finding the degree of a polynomial and the sign of its lead coefficient when you're given a graph

finding the local max or min from a graph

finding intervals where a graph is increasing or decreasing

determining where a function is increasing or decreasing

6 examples of finding domain and range from a graph

domain and range using inverval notation

more domain and range in interval notation

domain and range from a graph

more domain and range from a graph

a few more domain and range examples from graphs

finding x- and y-intercepts of a polynomial function - one example

finding x-and y-intercepts of a polynomial function - another example

using x- and y-intercepts to graph a polynomial function

  3.5-3.9 review worksheet  
  4.1 worksheet

midpoint and distance formulas

distance and midpoint formulas

more explanations and examples of using the distance and midpoint formulas

4.2 notes 4.2 worksheet

writing the equation of a circle when given the center and radius

two examples of writing the equation of a circle from the center and radius

finding the center and radius of a circle when given the equation in standard form

using completing the square to change the equation of a circle to standard form so that you can find the center and radius

another example of how to change the equation of a circle to standard form so that you can find the center and radius

4.3 notes (day 1 of parabolas) 4.3 worksheet

changing the equation of a parabola to vertex form

three examples of changing to vertex form

deciding whether a horizontal parabola opens left or right

finding direction a parabola opens, vertex, and includes axis of symmetry and comparable width to a parent function

example of finding vertex and direction for a parabola

4.3 notes (day 2 of parabolas) 4.3 worksheet

more on graphing parabolas, although what we call (1/4c), she calls (1/4p)

more on graphing parabolas-- what we call (1/4c), he calls (1/4a) instead

more on graphing parabolas-- we use 4c and this guy uses 4p. Also, we use a fraction (1/4c) but he uses 4p on the other side of the equation.

graphing a parabola and finding the focus and directrix, but he uses 4p where we call it 4c instead

graphing a parabola with finding focus and directrix, but he uses 4p where we use 4c and he puts the 4p on the other side from where we usually have it

4.4 (working backward) notes 4.4 worksheet  
  4.1-4.4 review worksheet  
   

OK, first a little rant. I see a lot of people (in person, and online) pronounce certain words or make certain words plural in ways that grate on my ears. Here's what I mean:

word what some people do (that I find strange or incorrect) what I think it should be (and what I use or say in class)
focus spell the plural "focii" spell the plural "foci"
foci pronounce it with a "hard c" like a k pronounce it with a "soft c" like an s
vertex pronounce the singular "vertice", as though they took the "s" off the plural form, "vertices" pronounce the singular (and spell it) as vertex
vertex write the plural form as "vertexes" write the plural form as "vertices"
matrix pronounce the singular "matrice", as though they took the "s" off the plural form, "matrices" pronounce the singular (and spell it) as matrix
matrix write the plural form as "matrixes" write the plural form as "matrices"

OK, rant over.

Day 7 of Unit 4 notes Day 7 Ellipse 10.3 - Day 1 WS

great introduction to ellipses

somewhat long video (about 27 minutes), but great information and explanation of ellipse information

even longer video with really good explanations of information about ellipses

two examples of graphing ellipses, including changing from general form to standard form by completing the square

one example of changing from general form to standard form by completing the square and then graphing

  Day 8 Ellipse 10.3 - Day 2 WS

Be sure to look at the videos for Day 7 of Unit 8 just above this!!!!

getting the equation of an ellipse when given length of major axis and length of minor axis

example of finding the equation of an ellipse when given the foci and the endpoints of the minor axis

another example of finding the equation of the ellipse when given information about the major axis and minor axis

writing the equation of an ellipse when given the endpoints of the major axis and the endpoints of the minor axis

Day 9 of Unit 4 notes Day 9 Hyperbolas 10.4 Day 1 WS

nice intrduction to hyperbolas

another nice introduction to hyperbolas, with an example centered at (0,0)

a couple examples of graphing hyperbolas with the vertices, foci, and asymptotes

great 10 minute introduction and 2 examples

a few examples of graphing hyperbolas

nearly 36 minutes, but a good intro, explanation, and a few examples of hyperbolas

Day 10 of Unit 4 notes Day 10 Hyperbolas 10.4 Day 2 WS

write the equation of a hyperbola when given the foci and the endpoints of the transverse axis

another example of finding the equation of a hyperbola from information about it

example of writing the equation of a hyperbola when given the vertices (endpoints of the transverse axis) and the length of the conjugate axis

another example of writing the equation of a hyperbola when given the vertices (endpoints of the transverse axis) and the length of the conjugate axis

Day 12 of Unit 4 notes Day 12 Identifying Conics Worksheet 10.6

Short video of how to identify conics

more examples of classifying conics

more classifying conics

Another person reviewing how to identify conics

Another way to classify conics

20 minute AWESOME review of conics and how to identify conics

Hour and 19 minute review of all the conics and how to graph them

Day 13 of Unit 4 notes Day 13 Nonlinear Systems Worksheet 10.7

example of a system of nonlinear equations solved by substitution and checked by graphing

solving a nonlinear system by substitution

example of a parabola intersecting a line in 2 points, solved by substitution

solving a system of conics by substitution and graphing (ignore the second example, which is a system of inequalities and not something we're going over)

example of an ellipse and a line by graphing and substitution

example of a circle and a line by substitution and graphing

solving a system of nonlinear equations by using the elimination method

another system of conics solved by elimination

one more example of using elimination to solve a system of nonlinear equations

more on using elimination to solve a system of nonlinear equations

 

  Day 15 Unit 4 Review - Conics (Part 2)  

 

Upcoming topics - these are videos I'll be organizing with particular sections or worksheets as we go through the year
construct absolute value functions

writing absolute value function equations from a graph

another example of writing the equation of an absolute value function from a graph

third example of writing the equation of an absolute value function from a graph

add and subtract radicals

Adding & Subtracting Radical Expressions

add and subtract radicals

transform other functions  
constructing quadratic functions given solutions, including complex solutions

writing an equation when given the roots or zeros

finding a quadratic equation given the roots

finding a quadratic function given the roots

factor and remainder theorems

the factor and remainder theorems

examples using the factor and remainder theorems

synthetic division, the factor theorem, and the remainder theorem

finding factors of polynomials with the factor and remainder theorems

using the factor and remainder theorems

factor polynomials

 

factor theorem, factoring a polynomial, and finding a polynomial from given roots

find zeros of a polynomial equation

finding all the zeros of a polynomial

finding the zeros of a polynomial

Finding all the zeros of a polynomial example

complex roots of polynomials

given one imaginary root, find all the other roots

given an imaginary root, find all the other roots

given one complex root, find all the other roots

using the quadratic formula and ending up with complex zeros

finding real and imaginary roots of a polynomial by factoring or recognizing quadratic form

finding real and complex roots by starting with the rational root theorem

starting with the rational root theorem to find all the roots of a polynomial

factoring over the complex numbers

factoring expressions using complex numbers

quadratic formula and completing the square to rewrite a polynomial using complex numbers

factoring a sum of squares by using imaginary numbers

nice review of factoring over complex numbers and also of writing a polynomial if you are given the roots

graphing polynomial functions graphing polynomials, including a look at end behavior, zeros, and multiplicity-- a longer one, but it covers it all
writing rational expressions as a quotient and rational remainder  
multiply and divide rational expressions  
finding the least common multiple of polynomials  
add and subtract rational expressions  
graphing rational functions  
transformations of rational functions  
solve rational equations  
rules of exponents  
simplifying expressions with rational exponents  
change between rational exponent form and radical form  
simplifying radical expressions  
simplify expressions with rational exponents  
adding, subtracting, muliplying, and dividing radical expressions  
rationalizing the denominator, including by using a conjugate  
solve equations involving rational exponents  
solve equations involving radical expressions  
Graph square root functions and inequalities  
transformations of radical functions  
solve exponential equations that do not require logarithms  
compound interest problems and exponential growth or decay problems  
convert equations between exponential and logarithmic form

introduction to logarithms

more about what logarithms are

use the inverse relationship between exponents and logarithms to solve simple exponential equations  
use the inverse relationship between exponents and logarithms to solve simple logarithmic equations  
expand and condense expressions using properties of logarithms  
solve problems by applying logarithms  
operations on functions  
compositions of functions  
find inverses of functions  
transformations of functions, including exponential and logarithmic functions