F-IF.4: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Day 3 (Concept) Review Domain of a function, , linear function, quadratic function New Cubic expressions and cubic functions Increasing and decreasing function Point of inflection Interval notation Rate of change makes a difference in the increasing or decreasing function Day 3 (Skills) Review Multiplying three binomials Graphing Linear equation New Graphing cubic function Describe behavior of a function for an interval given (in terms of increasing, or decreasing) Use the interval notation to describe for what values of x the graph is increasing or decreasing Day 3 (Material) Agile Mind Topic 4 *Exploring “quadratic and Cubics” P 1,2,3,6, and 7 Suggested assignment: SAS 3 Q14a-c GP P1-5 Moe Practice P 7 only *skip pages 4,5,8, and 9 However introduce interval notation on slide 3 F-BF.3. Identify the effect on the of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. Day 4 ( Concept) Review Rotation, Reflection New Definition of even and odd functions Definition of Line symmetry symmetry Day 4 ( Skills) Review Rotating shapes on a coordinate plane Reflecting lines over line New Sketching graphs intervals where the function is concave up or down and given the point of inflection Determining whether a function is even or odd graphically Determining whether a function is odd or even algebraically Day 4 (Material) Agile Mind Topic 4 * Exploring “Quadratic and Cubic” P10 - 11 SAS 3 Q15a – c GP 7 – 10 MP pg. only 11 Department provide supplements for identifying even and odd functions algebraically, graphically
or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Define the characteristics of function Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum Identify of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. Day 2 (Concept) Review X intercept and y intercept New: Definition End Behavior Meaning of Zeroes of a function Day 2 (Skills) Review Determine x intercept and y intercept from a table, graph New: Identify end/long term behavior of a function Determine number of zeroes in a function Graphing functions with zeroes ,the interval where function increases and decreases Comparing max and min from represented with graphs and tables ( Day 2 (Material) Mind Topic 5 Exploring “ Long – term behavior and zeroes ” P 1 – 9 SAS 3 Guided Practice P 1 – 11 More Practice Day 3 (Concepts) Review: Definition of X intercept s Definition of Polynomials Definition factors New: How the number of zeroes related to the Day 3 (Skills) Review: finding X intercept s from graphs and equations Definition of Polynomials factors trinomials use discriminants to see if there is a real solution New: Day 3 (Material) Agile Mind Topic 5 Exploring “ Higher polynomials ” P 1 – 7 SAS 4 Guided Practice note: skip page 1. additional
A.SSE.3: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. a. Factor a quadratic expression to reveal the zeros of the function it defines. A-APR.3: Identify of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial A-REI.11: Explain why the of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. Day1 (Concept) Review Quadratic and cubic function, Effect on the graph of f(x+k), f(x)+k, kf(x), f(kx) for the parent function f(x) Definition X intercepts New Understanding Real zeros and real roots on the graph Understanding how transformation can show zeroes of the quadratic function Definition of point of intersection vs. zero of a function Day 1 (Skills) Review Graphing quadratic and function,(by hand or graphing calculator) Using quadratic function to model problem situation Factoring trinomial to quadratic equation Using transformation to find the zeroes of the quadratic equation New Identifying Number of real zeroes and number of real roots Applying transformation to find roots of the polynomials Day 1 (Material) Agile Mind Topic 6 * Overview * Exploring “Quadratic Equation ” P 1-5 SAS 1 and 2 Suggested assignment: SAS 2 Q6 a – d and Q8, 9a-e, 10, and 11 a - b Guided Practice Pg. 1 - 4