Day 37 - Completing the Square - 10.08.14

Updates
  • Graphing Calculator needed for this course!
    • Recommended: TI-83
    • If you are unable to get a calculator, please email me as to why and I will try to get one for you.

Bell Ringer

Quadratic Functions
  1. What is the name of the graph of quadratic functions?

    1. paraboloid

    2. line

    3. curved line

    4. parabola

    5. none of the above

  2. What is the axis of symmetry of the following: y = -x2 - 6x + 15

    1. x = -3

    2. (-3, 24)

    3. x = 24

    4. x = 3

    5. none of the above

  3. What is the vertex point of the following: y = -x2 - 6x + 15

    1. x = -3

    2. (-3, 24)

    3. x = 24

    4. x = 3

    5. none of the above

  4. Does the following have minimum or maximum: y = -x2 - 6x + 15

    1. maximum

    2. minimum


Review
  • Prerequisites
    • Degree of a Polynomial
    • Zero Product Property
  • Quadratic Functions
    • Parabola
    • Minimum/Maximum
      • Finding by using algebra or graphing
    • Vertex
      • Finding by using algebra or graphing
    • Axis of Symmetry
      • x = -b / (2a)
    • Quadratic Roots

Lesson
  • Brainstorming Activity
    • Describe the difference between a parabola with a maximum and a parabola with a minimum value.
    • Give examples of two different parabolas that have the same vertex.
    • Explain how the axis of symmetry can help graph a quadratic function.
    • Checkpoints (page 542-543)
      • J - #4
      • K - #6
      • L - #12
      • M - #14
      • N - #44
      • O - #50

Exit Ticket
  • Posted on board at the end of the block.
Lesson Objective(s)
  • How can quadratic equations be solved using completing the square?

Standard(s)
  • Graphing Quadratic Functions
    • CC.9-12.F.IF.7a Graph linear and quadratic functions and show intercepts, maxima, and minima.
  • Solving Quadratic Equations
    • CC.9-12.A.REI.4 Solve equations and inequalities in one variable. Solve quadratic equations in one variable.
    • CC.9-12.A.REI.4b Solve quadratic equations by inspection (e.g., for x^2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.
  • Factored Form
    • CC.9-12.A.SSE.3a Factor a quadratic expression to reveal the zeros of the function it defines.
    • CC.9-12.F.IF.8a Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.
  • Completing the Square
    • CC.9-12.A.SSE.3b Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.
    • CC.9-12.A.REI.4a Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)^2 = q that has the same solutions. Derive the quadratic formula from this form.
    • CC.9-12.F.IF.8a Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.
  • Quadratic Formula
    • CC.9-12.A.REI.4a Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)^2 = q that has the same solutions. Derive the quadratic formula from this form.
  • Creating Quadratic Equations
    • CC.9-12.A.CED.1 Create equations that describe numbers or relationship. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.
  • Comparing Quadratics Function with Different Representations
    • CC.9-12.F.IF.9 Analyze functions using different representations. 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.
  • Quadratic Modeling
    • CC.9-12.F.LE.1 Construct and compare linear, quadratic, and exponential models and solve problems. Distinguish between situations that can be modeled with linear functions and with exponential functions.
    • CC.9-12.S.ID.6a Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models.
  • Complex Solutions of Quadratic Functions
    • CC.9-12.N.CN.7 Use complex numbers in polynomial identities and equations. Solve quadratic equations with real coefficients that have complex solutions.
    • CC.9-12.A.REI.4b Solve quadratic equations by inspection (e.g., for x^2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.

Mathematical Practice(s)
  • #1 - Make sense of problems and persevere in solving them
  • #2 - Reason abstractly and quantitatively
  • #4 - Model with mathematics
  • #5 - Use appropriate tools strategically
  • #7 - Look for and make use of structure



Past Checkpoints
  • Checkpoints
    • page 528-529
      • A - #8
      • B - #34
      • C - #36
      • D - #41-43
    • page 536-538
      • E - #16
      • F - #18
      • G - #20
      • H - #40
      • I - #50