How do we analyze, evaluate, solve, and graph quadratic functions?

Transcription

1 Topic: 4. Quadratic Functions and Factoring Days: 18 Key Learning: Students will be able to analyze, evaluate, solve and graph quadratic functions. Unit Essential Question(s): How do we analyze, evaluate, solve, and graph quadratic functions? Graphing Quadratic Functions 2.8.A2.B, 2.8.A2.D, 2.11.A2.A, 2.11.A2.C, A , A a, A , A , A , A Solving quadratic equations 2.1.A2.B, 2.5.A2.A, 2.5.A2.B, 2.8.A2.B, 2.8.A2.E, 2.8.A2.F, A , A Performing operations with square roots and complex numbers 2.1.A2.A, 2.2.A2.C, A , A , A , A How can we graph a quadratic function? (A) What methods can be used to solve a How do you simplify square roots in terms quadratic equation? (A) of i? (A) How do you determin, use, and/or interpret minimum and maximum values over a specified interval of a quadratic function? (ET) How do the solutions of quadratic equations relate to the graph of a quadratic function? (ET) How do you simplify/evaluate expressions involving imaginary numbers powers of i? (A) How do you determine the domain and range of a quadratic function? (ET) How can I use my knowledge of quadratics to solve real world problems? (A) How do you add and subract complex numbers? (A) What are the characteristics of a quadratic function (intervals of increasing/decreasing, intercepts, zeros)? (A) How do you multiply and divide complex numbers? (A) How can we use the vertex form of a quadratic function to identify and describe the effect of changing parameters of a quadratic function? (A) Standard Form, Parabola, Discrimminant, Axis of Symmetry, Zeros, Roots, Factor, Minimum, Maximum, vertex, vertex form, Quadratic formula, Zero product property, radical, radicand, rationalizing the denominator, conjugates, completing the square, discriminant, imaginary number i, complex number, complex conjugates, complex plane Page 1 of 2

2 Topic: 4. Quadratic Functions and Factoring Days: 18 Quadratic regressions 2.6.A2.C, 2.6.A2.E, A , A Write quadratic functions A How can you fit a quadratic function to a set of data? (A) How do you write a quadratic equation? (A) How do you make predictions using the quadratic equation or graph of regression models? (ET) quadratic regression Additional Information: Attached Document(s): Page 2 of 2

3 Vocab Report for Topic: 4. Quadratic Functions and Factoring Days: 18 Graphing Quadratic Functions Standard Form - Parabola - Discrimminant - Axis of Symmetry - Zeros - Roots - Factor - Minimum - Maximum - vertex - vertex form - Solving quadratic equations - Quadratic formula - Zero product property - radical - radicand - rationalizing the denominator - conjugates - completing the square - discriminant - Performing operations with square roots and complex numbers - imaginary number i - complex number - complex conjugates - complex plane - Quadratic regressions quadratic regression -

4 Topic: 12. Sequence and Series Days: 10 Key Learning: Arithmetic and geometric sequences and series can be used to find real life patterns. Unit Essential Question(s): How can sequence and series be used to model real life situations? Sequence 2.8.A2.C, A , A Series 2.8.A2.C, A What is an arithmetic sequence? (A) What is a geometric sequence? (A) How do you find the nth term of a sequence? (A) What are the similarities and differences between sequences and series? (A) What methods can be used to find the sums of arithmetic and geometric series? (A) Sequence, Common Difference, Common Ratio, Arithmetic, Geometric, nth term, recursion formula, explicit formula Convergent, Series, Divergent, Infinite Additional Information: Attached Document(s):

5 Vocab Report for Topic: 12. Sequence and Series Days: 10 Sequence Sequence - Common Difference - Common Ratio - Arithmetic - Geometric - nth term - recursion formula - explicit formula - Series Convergent - Series - Divergent - Infinite -

6 Topic: 7. Exponential and logarithmic functions Days: 15 Key Learning: Relate exponential functions and their applications to growth and decay. Unit Essential Question(s): What is the relationship between exponential functions and their inverse? Graphing exponential and logarithmic functions 2.8.A2.B, 2.5.A2.B, 2.5.A2.A, 2.1.A2.F, 2.8.A2.D, 2.8.A2.E, 2.11.A2.B, A , A , A , A , A , A , A Solving exponential and logarithmic equations 2.8.A2.B, 2.8.A2.F, A exponential and logarithmic regression 2.6.A2.C, 2.6.A2.E, A , A What are exponential functions and what How do you rewrite logarithmic How do you construct and calculate an are the characterisitics of their graphs? (A) expressions? (A) exponential or logarithmic regression? (A) What are the similarities and differences between exponential growth and decay functions? (A) What are real world applications of exponential functions? (ET) How do you solve exponential and logarithmic equations? (A) Why do you get extraneous solutions when solving logarithmic equations? (ET) How do you make predictions or draw conclusions on the value of a variable in a population based on the results of a sample? (ET) How do you evaluate and graph logarithmic functions? (ET) exponent, exponential function, exponential growth, exponential decay,, growth factor, asymptote natural base e, common logarithm, natural logarithm, exponential equation, logarithmic equation, extraneous solution Additional Information: Attached Document(s):

7 Vocab Report for Topic: 7. Exponential and logarithmic functions Days: 15 Graphing exponential and logarithmic functions exponent - exponential function - exponential growth - exponential decay - - growth factor - asymptote - Solving exponential and logarithmic equations natural base e - common logarithm - natural logarithm - exponential equation - logarithmic equation - extraneous solution -

8 Topic: 5. Polynomials and Polynomial Functions Key Learning: Unit Essential Question(s): What are the characteristics of a polynomial function? Properties of Exponents 2.1.A2.D, 2.8.A2.B, 2.8.A2.E, A , A , A Performing operations with polynomials A , 2.1.A2.B Graphs of Polynomial Functions A , A a, A , 2.8.A2.D, A , A How do you use the properties of exponents to simplify expressions involving powers? (A) How do you add, subtract, multiply and divide polynomials? (A) What are the characteristics of a polynomial functions (i.e. domain, range, intervals of increasing and decreasing, maximums, minimums, zeros, intercepts)? (A) How do you use exponential expressions to represent rational numbers? (A) How do you factor polynomials? (A) scientific notation polynomial functions, end behavior Solving Polynomial Equations and Finding Zeros 2.8.A2.B, 2.8.A2.F Cubic Regression 2.6.A2.C, 2.6.A2.E, A , A How do the solutions of a polynomal equation relate to the graph of the related polynomial function? (A) How do you draw, identify, find and/or write an equation for a polynomial regression (cubic or quartic)? (A) How do you make predictions using the equations or graphs of regression models? (ET) rational zero cubic regression, quartic regression Additional Information: Attached Document(s):

9 Vocab Report for Topic: 5. Polynomials and Polynomial Functions Properties of Exponents scientific notation - Graphs of Polynomial Functions polynomial functions - end behavior - Solving Polynomial Equations and Finding Zeros rational zero - Cubic Regression cubic regression - quartic regression -

10 Topic: 1. Rewrite Formulas and Equations Key Learning: Use algebraic processes to solve a formula for a given variable and then determine how a change in one variable relates to a change in a second variable. Unit Essential Question(s): How do you rewrite and evaluate formulas and equations? Rewriting formulas 2.3.A2.C, A Evaluating formulas 2.3.A2.E, A How do you use algebraic processes to solve a formula for a given variable? (e.g., solve d = rt for r) (A) How do you determine how a change in one variable relates to a change in a second variable (e.g., y = 4/x; if x doubles, what happens to y?) (A) formula Additional Information: These topics can be found in the textbook in 1.4 Determining how a change in one variable relates to a change in a second variable is not addressed in our textbook, but in many of the exercises, after rewriting a formula and evaluating for a given value, you can ask questions about determining how a change in one variable relates to a change in a second variable. Attached Document(s):

11 Vocab Report for Topic: 1. Rewrite Formulas and Equations Rewriting formulas formula -

12 Topic: 8. Rational Functions Key Learning: Unit Essential Question(s): How can you use rational functions to model real-life situations? Graphs of Rational Functions 2.8.A2.D, A , A , A , A Performing operations with rational expressions A Solving Rational Equations 2.8.A2.F, A How do you graph rational functions using How do you multiply and divide rational How do you solve rational equations? (A) transformations? (A) expressions? (A) What are the characteristics of a graph of a rational function? (A) How do you add and subtraction rational expressions? (A) How do you simplify a rational expression? (A) What type of equations have extraneos solutions? (ET) When can you cross multiply to solve a rational equation? (A) rational function, domain, range, asymptote, complex fraction cross multiplying end behavior Additional Information: Attached Document(s):

13 Vocab Report for Topic: 8. Rational Functions Graphs of Rational Functions rational function - domain - range - asymptote - end behavior - Performing operations with rational expressions complex fraction - Solving Rational Equations cross multiplying -

14 Topic: 10. Counting Methods and Probability Key Learning: How can you count the number of possible outcomes of an event or the number of ways to complete a task? Unit Essential Question(s): Permutations and Combinations A Probabilities and Odds 2.7.A2.A, 2.7.A2.C, 2.7.A2.E, A , A How is the "Fundamental Counting Principle" similar and different from a Permutation or Combination? (ET) How is a Permutation and Combination similar and different? (ET) How can you find the likelihood that an event will occur? (A) How is probability different from odds? (ET) How do you find the probability of a compound event? (A) How do you find the probability of independent and dependent events? (A) How do you use combinations, permutations, and the fundamental counting principle to solve problems involving probability? (ET) How do you use odds to find probability and/or use probability to find odds? (ET) Permutation, Pascal's Triangle, Binomial Theorem, Combination, Factorial Probability, Odds, Compound Event, Overlapping Events, Disjoint or mutually exclusive events Additional Information: Attached Document(s):

15 Vocab Report for Topic: 10. Counting Methods and Probability Permutations and Combinations Permutation - Pascal's Triangle - Binomial Theorem - Combination - Factorial - Probabilities and Odds Probability - Odds - Compound Event - Overlapping Events - Disjoint or mutually exclusive events -