1. Know - Understand - Do Organizer

  • Topic:#2 Quadratic Expressions, Functions, and Equations
  • Subject(s):
  • Days:25
  • Grade(s):9, 10, 11, 12
Which standards are students learning in this unit?
Know:

 Vertex of a Parabola


Axis of Symmetry


Translations


Standard Form of a Quadratic


Vertex Form of a Quadratic


Factoring Quadratics


Complex Numbers


Completing the Square


Quadratic Formula

Understand:

Quadratic functions represent a family of curves with complex solutions.



Quadratic equations can be solved using a variety of techniques.

Do:
A2.1.1.1.1 -- EssentialSimplify/write square roots in terms of i (e.g., √‐24 = 2i√6).
A2.1.1.1.2 -- EssentialSimplify/evaluate expressions involving powers of i (e.g., i 6 + i 3 = ‐1 – i).
A2.1.1.2.1 -- EssentialAdd and subtract complex numbers (e.g., (7 – 3i) – (2 + i) = 5 – 4i).
A2.1.1.2.2 -- EssentialMultiply and divide complex numbers (e.g., (7 – 3i)(2 + i) = 17 + i).
A2.1.2.2.1 -- EssentialFactor algebraic expressions, including difference of squares and trinomials. Note: Trinomials limited to the form ax2+bx+c where a is not equal to 0.
A2.1.3.1.1 -- EssentialWrite and/or solve quadratic equations (including factoring and using the Quadratic Formula).
A2.2.1.1.4 -- EssentialIdentify and/or determine the characteristics of an exponential, quadratic, or polynomial function (e.g., intervals of increase/decrease, intercepts, zeros, and asymptotes).
A2.2.2.1.1 -- EssentialCreate, interpret, and/or use the equation, graph, or table of a polynomial function (including quadratics).
A2.2.2.1.3a -- EssentialDetermine, use, and/or interpret minimum and maximum values over a specified interval of a graph of a function.
A2.2.3.1.1 -- EssentialDraw, identify, find, interpret, and/or write an equation for a regression model (lines and curves of best fit) for a scatter plot.
A2.2.3.1.2 -- EssentialMake predictions using the equations or graphs of regression models (lines and curves of best fit) of scatter plots.
2.8.A2.D -- EssentialFUNCTIONS - Demonstrate an understanding and apply properties of functions (domain, range, inverses) and characteristics of families of functions (linear, polynomial, rational, exponential, logarithmic).

A2.1.1.1.1 - Simplify/write square roots in terms of i (e.g., √‐24 = 2i√6).
A2.1.1.1.2 - Simplify/evaluate expressions involving powers of i (e.g., i 6 + i 3 = ‐1 - i).
A2.1.1.2.1 - Add and subtract complex numbers (e.g., (7 - 3i) - (2 + i) = 5 - 4i).
A2.1.1.2.2 - Multiply and divide complex numbers (e.g., (7 - 3i)(2 + i) = 17 + i).
A2.1.2.2.1 - Factor algebraic expressions, including difference of squares and trinomials. Note: Trinomials limited to the form ax2+bx+c where a is not equal to 0.
A2.1.3.1.1 - Write and/or solve quadratic equations (including factoring and using the Quadratic Formula).
A2.2.1.1.4 - Identify and/or determine the characteristics of an exponential, quadratic, or polynomial function (e.g., intervals of increase/decrease, intercepts, zeros, and asymptotes).
A2.2.2.1.1 - Create, interpret, and/or use the equation, graph, or table of a polynomial function (including quadratics).
A2.2.2.1.3a - Determine, use, and/or interpret minimum and maximum values over a specified interval of a graph of a function.
A2.2.3.1.1 - Draw, identify, find, interpret, and/or write an equation for a regression model (lines and curves of best fit) for a scatter plot.
A2.2.3.1.2 - Make predictions using the equations or graphs of regression models (lines and curves of best fit) of scatter plots.

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