Embedded Files
Opening Day Handout
Unit 1 - Functions
Lesson 1 Relations and Functions Blank Notes | Completed Notes
In today’s lesson, we discussed the difference between relations and functions. We also looked at different ways to represent functions and how to determine the domain and range for a function. Finally, we used the vertical line test to determine if a relation is a function and showed how to evaluate a function for a particular x-valuie.
Lesson 2 Domain and Range Blank Notes | Completed Notes
Today, we discussed how to find the domain for various types of functions (polynomial, radical, rational, etc.). We also used technology to evaluate these sets when the function was overly complicated.
Lesson 3 Parent Functions and Transformations Blank Notes | Completed Notes
In this lesson, we explored how to use transformations to change the graph of a parent function. We also found equations for already transformed functions based on the parent function.
Quiz after these topics
Lesson 4 Features of Functions Blank Notes | Completed Notes
In today's lesson, we examined how to use to find the following (using technology where appropriate): coordindates of intercepts and extrema, intervals of increasing and decreasing, intervals of positive and negative values, equations of any asymptotes, and the end behavior of a function. We also used technology to determine the coordinates of intersection of two graphs.
Lesson 5 Average Rate of Change Blank Notes | Completed Notes
In this lesson, we learned how to calculate the average rate of change for a function over an interval, and how to interpret that rate of change as the slope of the secant line which connects those two points on the function.
Lesson 6 Regressions Blank Notes | Completed Notes | Video Walkthrough
In today’s lesson, we used data to find a line of best fit and interpret its slope and intercept. We discussed correlation, how to make predictions, and how technology (like a graphing calculator or spreadsheet) helps us model data trends.
Unit 1 Test after these topics
Unit 2 - Quadratic Functions
Lesson 1 Vertex Form Blank Notes | Completed Notes
Today, we'll examine vertex form of a parabola. We'll graph parabolas, construct a model given a vertex and another point on the parabola, and convert such functions to standard form. We'll also examine what the symmetry of a parabola can tell us about additional points which lie on the parabola.
Lesson 3 Standard Form Blank Notes | Completed Notes
In today's lesson, we'll examine parabolas whose equations are presented in standard form. We'll also determine a shortcut for finding the vertex of a parabola in standard form as well its y-intercept. We'll continue to graph and analyze parabolas.
Lesson 4 Intercept Form Blank Notes | Completed Notes
Additional Practice | Completed
In today's lesson, we look at the connection between the factored (intercept) form of a parabola, and its roots. We'll also make connections to the other two forms of a parabola previously studies, and create models for quadratics given its intecepts and another point on the parabola.
Quiz after these topics Review of Topics | Completed
Lesson 5 Solving Systems of Linear Equations Blank Notes | Completed
In today's lesson, we will learn how to solve a 3-variable system using technology. We'll also discuss how these systems can be used to find the equation of a quadratic containing three points.
Lesson 6 Modeling with Quadratics Blank Notes | Completed
In today's lesson, we'll discuss how to create the equation of a quadratic with given quantities. In many ways, we have already discuss this throughout the Unit! However, today's lesson is a summary of these methods, and we'll stress the importance of knowing what information is provided and how to use that the come up with the appropriate model for the particular quadratic function.
Spiral Quiz or Graded Assignment after these topics
Unit 3 - Quadratic Equations
Lesson 1 Solving Quadratic Equations by Factoring Blank Notes | Completed Notes
Today, we'll look at how to generate solutions to quadratic equations by factoring. This will include a review of factoring usingthe GCF, factoring quadratics in standard form (using a variety of methods), using the "substititution" method for factoring, and using the difference of two squares method to factor appropriate expressions. Finally, we'll take a look at the "square root" method for solving quadratics.
Lesson 2 Solving Nonlinear Systems of Equations Blank Notes | Completed Notes
In today's lesson, we will learn how to solve systems of equations that contain either two quadratics, or a combination of a quadratic and linear function. We'll solve using technology and also by using substitution.
Lesson 3 Completing the Square Blank Notes | Completed Notes
In today's lesson, we will examine an algebraic method for solving quadratics (which always works, unlike factoring). We'll also use this method to convert quadratics to vertex form from standard form.
Lesson 4 Imaginary Numbers Blank Notes | Completed Notes
Today, we will look at the "imaginary" numbers, which provide solutions to quadratic equations that have no "real" solutions.
Lesson 5 The Quadratic Formula Blank Notes | Completed Notes
Today, we will look at a formulaic approach to solving quadratic equations, known as the Quadratic Formula. We'll derive the formula and apply it to solving quadratics.
Graded Assignment after these topics
Unit 4 - Polynomials
Lesson 1 Polynomial Functions Blank Notes | Completed Notes
In this lesson, we'll learn what a polynomial is, what is "standard form" of a polynomial, and also classify polynomials by their number of terms and degree. We'll also discuss the end behavior of polynomials and sketch polynomials with particular characteristics.
Lesson 2 Polynomials and Zeros Blank Notes | Completed Notes
Today, we'll discuss the meaning of x-intercepts, zeros, and roots. We'll also construct polynomials when the zeros are known, examine the irrational and complex conjugate theorems, and construct sketches of graphs given the zeros, their multiplicities, and the graph's end behavior.
Graded Assignment after these topics Blank Review | Completed Review
Lesson 3 Operations with Polynomial Function Blank Notes | Completed Notes
In this lesson, we'll talk about how to perform mathematical operations on functions, such as addition, subtraction, multiplication, and division--and look at an interesting type of problem which involves finding a particular coefficient of a term.
Lesson 4 Polynomial Division Blank Notes | Completed Notes
Today, we'll discover how to divide polynomials using long division and synthetic division. We'll also use the synthetic division algorithm to use a process call synthetic substitution. Finally, we'll discuss how to know if a divisor of the form (x-k) is a factor of a given polynomial, using the Remainder Theorem and the Factor Theorem.
Lesson 5 Factoring Polynomials Blank Notes | Completed Notes
Today, we'll review factoring methods for factoring polynomials. We'll also discuss how to factor higher-degree polynomials when one or more roots are already given.
Lesson 6 Solving Polynomial Equations Blank Notes | Completed Notes
Today, we will study the Fundamental Theorem of Algebra, and use strategies to help solve polynomial equations, including the use of technology, factoring, and synthetic division.
Lesson 7 Solving Polynomial Inequalities Blank Notes | Completed Notes
In today's lesson, we will discuss how to solve polynomial inequalities by factoring the polynomial, conducting a sign test, and interpreting the results.
Unit 5 - Radicals and Rational Exponents
Lesson 1 Properties of Exponents Blank Notes | Completed Notes
Today, we'll review how to simplify expressions that contain exponents, including: multiplying powers, dividing powers, "power to a power", and zero and negative exponents, among others.
Lesson 2 Rational Exponents Blank Notes | Completed Notes
In this lesson, we'll explore the meaning of a rational exponent ("power over root"), and continue working with properties of exponents. We'll also connect this topic to the idea of rewriting an exponential expression as a radical and vice versa.
Lesson 3 Simplifying Radicals Blank Notes | Completed Notes
Today, we'll learn how to simplify radicals, whether the index is 2, 3, 4, ... or really anything. We'll also discuss when it's necessary to use absolute value bars in your answer.
MIDTERM REVIEW PACKET Blank | Answer Key
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