Unit 2--Algebra: Polynomial Functions

February 8 - March 2, 2012


2/8-9/2012

  • Raider Flashback (warm up)
  • Lesson 2.1 Evaluate and Graph Polynomial Functions pp. 66-68 (MM3A1b, MM3A1c, MM3A1d)
    • Key Concept- Polynomial functions can be identified by the degree of the polynomial and evaluated using either direct substitution or synthetic substitution. The end behavior of the function and a table of values can be used to graph polynomial functions.
    • Questions to think about...
      1. What is the standard form of a linear equation? What is its degree? How many turning points does a linear function have?
      2. What is the standard form of a quadratic equation? What is its degree? How many turning points does a quadratic function have?
      3. What do you think will happen to a graph as the degree of the polynomial function increases?
    • Common Errors...
      • When using synthetic substitution, students may forget to write zeros for the missing terms of a polynomial.
  • Classwork: Guided Practice Problems 1-7
  • Homework: Workbook page 79-80(1-21)evens
  • Class Notes: post after class

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2/10/2012

  • Raider Flashback (warm up)
  • Lesson 2.2 Translate Graph of Polynomial Functions pp. 71-73 (MM3A1a, MM3A1c, MM3A1d)
    • Key Concept- Simple polynomial functions can be graphed as vertical and horizontal translations of parent functions.
    • Questions to think about...
      • Graph y= x cubed
      • Use a table of values to graph the function. How does the graph compare with that of y= x cubed
        • y = (X-2)cubed
        • y = X cubed + 5
        • y = (X-2)cubed + 5
      • Make a conjecture about how "h" and "k" affect the graph of y = (h-k)cubed + k
    • Common Errors...
      • Some students may be confused about the effects of h and k on the graph of a polynomial function.
  • Classwork: Guided Practice Problems 1-12
  • Homework: Workbook page 84-85(every 3 starting with problem 3)
  • Class Notes: post after class
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2/13/2012
  • Raider Flashback (warm up)
  • Lesson 2.3 Factor and Solve Polynomial Equations pp. 76-77 (MM3A3b, MM3A3d)
    • Key Concept- Polynomials can be factored using several techniques including factoring by finding a common monomial factor, factoring using sum and difference of two cubes, and factoring by grouping. The zero product property can be used to solve some higher degree polynomial equations.
    • Questions to think about...
      • Rewrite the equation X(X-2)(X+8)=96 in standard form (ax cubed + bx squared +cx +d = 0).
      • Factor the ax cubed + bx squared part of the equation. What is the result? Then factor the cx + d part of your equation. What is the result? What similarity do you notice?
    • Common Errors...
      • Some students stop factoring before a polynomial is fully factored. Students remember to examine you answer for expressions that may be factorable.
  • Classwork: Guided Practice Problems 1-7
  • Homework: Workbook page 89-90 (every 3 starting with problem 1)
  • Class Notes:

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2/14/2012

  • Lesson 2.4 Solve Polynomial Inequalities pp. 81-82 (MM3A3c)
    • Key Concept- Polynomial inequalities can be solved algebraically or graphically. To solve a polynomial inequality algebraically, solve the corresponding equation and test the point in each resulting interval to see if it satisfies the inequality. To solve a polynomial inequality graphically, graph the corresponding polynomial function and see where the function is above and below the x-axis
    • Questions to think about...
      • Graph the polynomial function y = 2x cubed + 9x squared - 5x and identify the x-intercepts
      • For what values of x is the value of the function less than 0? How does your answer relate to the inequality 2x cubed + 9x squared -5x < 0?
      • For what values of x is the value of the function greater than 0? How does your answer relate to the inequality 2x cubed + 9x squared -5x > 0?
    • Common Errors...
      • Students may have difficulty with the use of parentheses and brackets in the interval notation.
  • Classwork: Guided Practice Problems 1-7
  • Homework: Workbook page 94-95(1-25)evens
  • Class Notes:

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2/15-16/2012
  • Raider Flashback
  • Quiz 1 & 2 section 2.1-2.4
  • Lesson 2.5 Apply the Remainder and Factor Theorems pp.85-86 (MM3A3a)
    • Key Concept- Polynomial long division and synthetic division are two techniques used to divide polynomials. The factor theorem can be used to factor polynomial and find the zeros of polynomials.
    • Questions to think about...
      1. Use long division to divide 3105 by 12. What is the dividend? The divisor? The quotient? The remainder?
      2. How can you use multiplication to check the result of division?
    • Common Errors...
      • Remember students that when using synthetic division, you must write the opposite of the constant term of the divisor.
  • Classwork: Guided Practice Problems 1-9
  • Homework: Workbook page 99-100 (1-22) odds
  • Class Notes: post after class

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2/17 & 2/20/2012-- NO SCHOOL

2/21-22/2012
  • Raider Flashback
  • Review Lesson 2.5
  • Lesson 2.6- (MM3A3a, MM3A3d)
    • Key Concept-
      • The rational zero theorem is used to list the possible rational zeros of polynomial functions. Actual zeros can be found by testing the possible rational zeros using synthetic division and sketching the graph of the function to help choose values of zero to test.
    • Questions to think about...
      • How do you identify the leading coefficient and identify the solution
    • Common Errors...
      • When listing possible rational zeros, it is important to simplify fractions and eliminate duplicate
    • Classwork: Guided Examples 1-3, Practice Problems 1-7
    • Homework: Workbook 2.6- odd problems
  • Class Note

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2/23-24/2012
  • Raider Flashback
  • Review Lesson 2.6
  • Lesson 2.7 (MM3A3a, MM3A3d)
    • Key Concept- Thr fundamental theorem of algebra can be used to determine the number of solutions of an equation. Descartes' rule of signs can be used to determine the possible number of positive, negative, and imaginary zeros of a function.
    • Questions to think about...
      • If the discriminant is less than zero, how many and what type if solutions does a quadractic equation have?
      • What is a complex conjugate?
    • Common Errors...
      • When applying Descartes' rule of signs, students may have trouble calculating f(-x). Remind students that (-x)^n=x^n when n is even and (-x)^n=-x^n when n is odd.
  • Classwork: Examples 1-3, Practice Problems 1-7
  • Homework: Workbook 2.7 choose three problems from each of the four section given yourself 12 homework problems
  • Class Notes
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2/27-28/2012
  • Raider Flashback
  • Review Lesson 2.7
  • Lesson 2.8 (MM3A1b, MM3A1d)
    • Key Concept
      • The x-intercept of a polynomial function, a table of values, and the end behavior of the function can be used to graph the function. The turning points of a graph occur at the local minimums and local maximums of the function.
    • Questions to think about...
      • A point on the graph of a polynomial function is a turning point if it is higher or lower than all of the nearby points on the graph.
    • Common Errors...
      • Students may erroneously believe that a polynomial function of degree n has exactly (n-1) turning points. Remind students that this is true only if a function also has n real zeros.
  • Classwork: Examples 1-3, Guided Practice Problems 1-3
  • Homework: Workbook 2.8 even problems
  • Class Notes
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2/29/2012
  • Raider Flashback
  • Test Review Unit 2 Test in the book p.105(1-17) working in groups of five
  • Test Review Unit 2 Test in the book p.105(18-31) working in groups of five

3/1/2012

  • Raider Flashback
  • Unit 2 Test part A (postponed until after midterm finals)
  • Studying for MIDTERM FINALS

3/2/2012
  • Raider Flashback
  • Unit 2 Test part B (postponed until after midterm finals)
  • Studying for MIDTERM FINALS

Unit 2 Test will be giving after the midterm final next week