Essential Questions:
*What are the advantages of a quadratic function in vertex form? In standard form?
*How is any quadratic function related to the parent quadratic function y = x2
*How are the real solutions of a quadratic equation related to the graph of the related quadratic function?
Students will identify the vertex, axis of symmetry, maximum or minimum, domain and range, and translations of a quadratic funtion. Students will graph quadratic functions with and without graphing aids. Students will compare translations to the parent quadratic function. Students will identify the x-intercepts of the graphs of related quadratic functions.
1. 3-1: Quadratic Functions and Transformations
Objective: To identify and graph quadratic functions.
Skills: [These are the list of skills that will be covered in each days lessons] graphing a function of the form f(x)=x^2; exploring vertex form; graphing translations of f(x) = x^2; interpreting Vertex Form https://drive.google.com/a/es-impact.org/folderview?id=0B-waw_otYSTNWkI0Vi1LTUpCX2s&usp=sharing Homework: None
1
Dec
2. 3-1: Quadratic Functions and Transformations
Objective: To graph quadratic functions. To justify claims using mathematical evidence in written form.
Skills: using Vertex form y=a(x-h)^2 + k; writing a quadratic function in vertex form; math justification paragraphs with evidence. LESSON CHECK: [Lesson checks are used for the students to self-assess their understanding of the lesson. These are not grading for correctness but are used for an "informal" assessment by myself.] Homework: Finish Example 5: Writing Quadratic Functions. You will need the claim/evidence paragraph for class Monday. Also, there are iXL skills to be completed. The skills have been highlighted on iXL. Please complete 10 problems from each skill by Monday.
2/3
Dec
3. 3-2: Standard Form of a Quadratic Function
Objective: To graph quadratic functions written in standard form.
Skills: graphing a function of the form y=ax^2 + bx + c; converting standard form to vertex form (and vertex form to standard form) Homework: Finish Example 5 problem. Be sure to have your claim/evidence paragraph done for Monday's class. There are iXL skills highlighted on the website. Please complete 10 problems from each skill.
7
Dec
4. 3-2: Standard Form of a Quadratic Function
Objective: To interpret a quadratic equation in a real world context.
Skills: interpreting a quadratic graph; annotating and solving word problems LESSON CHECK Homework:
8
Dec
5. 3-3: Modeling with Quadratic Functions
Objective: to model data with quadratic functions.
Skills: comparing quadratic models LESSON CHECK Skills: factoring [students will be given a pre-assessment to evaluate their prior knowledge of factoring] Homework
9/10
Dec
Objective: To find common and binomial factors; to factor special quadratic expressions
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14
Dec
Objective: To find common and binomial factors; to factor special quadratic expressions
Skills: factoring a perfect square trinomial; factoring a difference of two squares LESSON CHECK Homework: ***Study for Quiz***
15
Dec
8. Group Quiz - Unit 3 Quiz #1
Lesson - 3-1; 3-2; 3-3; 3-4
Students will be placed into groups of 3-4 where they will review their knowledge of the skills learned in the current Unit. Angry Birds Work Time Homework: Angry Birds ***Happy Holidays***
16/17
Dec
9. Quiz/Unit Review
Objective: to identify and correct any misconceptions from the beginning of the Unit.
Students will complete Quiz Corrections. Homework: complete Quiz Corrections.
5
Jan
Objective: to solve quadratic equations by factoring; by graphing
Skills: simplify radicals; solving a quadratic equation by factoring; solving a quadratic equation with tables; solving a quadratic equation by graphing; using a quadratic equation. LESSON CHECK Homework
6/7
Jan
11. 3-A: Intercept Form
Objective: to write a quadratic equation, given its zeros/roots.
Activity: Students will write quadratic functions, given its zeros in factored and standard form; find the sum and product of the roots of a quadratic equation in standard form. LESSON CHECK Homework
11
Jan
12. 3-6: Completing the Square
Objective: to solve equations by completing the square.
Skills: solving by finding square roots; solving a perfect square trinomial equation; completing the square Homework
12
Jan
13. 3-6: Completing the Square
Objective: to rewrite functions by completing the square.
Skills: solving by completing the square; writing in vertex form LESSON CHECK ((Angry Birds Work Time)) Homework
13/14
Jan
Objective: to derive the quadratic formula; to solve equations using the quadratic formula
19
Jan
Objective: to investigate and use different methods to solve quadratic inequalities.
Skills: solve by factoring; solve by graphing related functions; solve by solving the related function. Homework
1
Feb
Objective: to determine the number of solutions by using the discriminant.
Skills: using the discriminant; using the discriminant to solve a problem LESSON CHECK ((Angry Birds Work Time)) Homework: Study for Quiz
20/21
Jan
17. Unit 3 Quiz #2
3-5, 3-6, 3-7
25
Jan
18. 3-8: Complex Numbers
Objective: to identify, graph, and perform operations with complex numbers.
Skills: simplifying a number using i; identify complex numbers (real & imaginary parts); graphing in the complex number plane; adding and subtracting complex numbers; multiplying complex numbers Homework
26
Jan
19. 3-8: Complex Numbers
Objective: to perform complex number operations; to find complex number solutions of quadratic equations
Skills: multiplying complex numbers; dividing complex numbers; factoring using complex conjugates; finding imaginary solutions LESSON CHECK
27/28
Jan
Objective: to solve and graph systems of linear and quadratic equations/inequalities
Skills: solve a linear-quadratic system by graphing; solving a linear-quadratic system using substitution; solving a linear-quadratic system of inequalities. LESSON CHECK Homework
2
Feb
Objective: to clarify any misconceptions with Unit 3 Quadratic skills/concepts
Rotation Stations based on Traffic Lighting (students will have self-assessed their knowledge of the skills to review the necessary skills during this review session) Homework: ***Study for Unit Test ***
3/4
Feb
22. Unit 3 Test
Objective: students will apply their knowledge of Quadratics to Unit test.
Good Luck!
5
Feb
23. Project Work Time
Students will be given until Feb 18, of in-class time to complete their Angry Birds projects. Students will have the opportunity to get peer feedback from other students. PROJECTS DUE FEBRUARY 22 - IN-CLASS!
8-19
Feb
24. ANGRY BIRDS PROJECTS DUE!
Students will submit their Angry Birds Projects. Any late projects will have points deducted. End of Day = -5% Each additional day = - 10% Cannot submit projects past March 7th
22
Feb