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Unit 3-1: Factoring Quadratics (Doc, PDF, Key)
Georgia Standards of Excellence (Click to Expand)
MGSE9-12.A.SSE.2: Use the structure of an expression to rewrite it in different equivalent forms. For example, see x^4 – y^4 as (x^2)^2 - (y^2)^2, thus recognizing it as a difference of squares that can be factored as (x^2 – y^2) (x^2 + y^2).

MGSE9-12.A.SSE.3: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.


MGSE9-12.A.SSE.3a: Factor any quadratic expression to reveal the zeros of the function defined by the expression


Video Lessons: (p1, p2, p3, p4)

Sample Quiz: (Interactive, PDF)

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Unit 3-2: Solving Basic Quadratic Equations (Doc, PDF, Key)
Georgia Standards of Excellence (Click to Expand)
MGSE9-12.A.REI.4: Solve quadratic equations in one variable.

MGSE9-12.A.SSE.3a: Factor any quadratic expression to reveal the zeros of the function defined by the expression


MGSE9-12.A.REI.4b: Solve quadratic equations by inspection (e.g., for x^2= 49), taking square roots, factoring, completing the square, and the quadratic formula, as appropriate to the initial form of the equation (limit to real number solutions).

MGSE9-12.A.CED.1: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from quadratic functions.

MGSE9-12.A.CED.2: Create linear and quadratic equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. (The phrase “in two or more variables” refers to formulas like the compound interest formula, in which A = P(1 + r/n)nt has multiple variables.)

MGSE9-12.F.BF.1: Write a function that describes a relationship between two quantities.


Video Lessons: (p1a, p1b, p2a, p2b, p3, p4)

Sample Quiz: (Interactive, PDF)

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Unit 3-3: Completing the Square (Doc, PDF, Key)
Georgia Standards of Excellence (Click to Expand)

MGSE9-12.A.SSE.3a: Factor any quadratic expression to reveal the zeros of the function defined by the expression

MGSE9-12.A.SSE.3b Complete the square in a quadratic expression to reveal the maximum or minimum value of the function defined by the expression.

MGSE9-12.A.REI.4: Solve quadratic equations in one variable.

MGSE9-12.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 ax^2 + bx + c = 0.

MGSE9-12.A.REI.4b: Solve quadratic equations by inspection (e.g., for x^2= 49), taking square roots, factoring, completing the square, and the quadratic formula, as appropriate to the initial form of the equation (limit to real number solutions).


Video Lessons: (p1a, p1b, p2a, p2b)

Sample Quiz: (Interactive, PDF)
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Unit 3-4: Quadratic Formula (Doc, PDF, Key)
Georgia Standards of Excellence (Click to Expand)
MGSE9-12.A.REI.4: Solve quadratic equations in one variable.

MGSE9-12.A.REI.4b: Solve quadratic equations by inspection (e.g., for x^2= 49), taking square roots, factoring, completing the square, and the quadratic formula, as appropriate to the initial form of the equation (limit to real number solutions).

MGSE9-12.A.CED.1: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from quadratic functions.

MGSE9-12.A.CED.2: Create linear and quadratic equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. (The phrase “in two or more variables” refers to formulas like the compound interest formula, in which A = P(1 + r/n)nt has multiple variables.)

MGSE9-12.F.BF.1: Write a function that describes a relationship between two quantities.

Video Lessons: (p1, p2a, p2b, p3, p4a, p4b)

Sample Quiz: (Interactive, PDF)


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Unit 3-5: Vertex Form of a Parabola (Doc, PDF, Key)
Georgia Standards of Excellence (Click to Expand)
MGSE9-12.A.SSE.3b Complete the square in a quadratic expression to reveal the maximum or minimum value of the function defined by the expression.

MGSE9-12.F.BF.3: Identify the effect on the graph 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.

MGSE9-12.F.IF.5: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

MGSE9-12.F.IF.7: Graph functions expressed algebraically and show key features of the graph both by hand and by using technology.

MGSE9-12.F.IF.7a: Graph quadratic functions and show intercepts, maxima, and minima (as determined by the function or by context).

MGSE9-12.F.IF.8: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

MGSE9-12.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. For example, compare and contrast quadratic

Video Lessons: (p1a, p1b, p2a, p2b, p3a, p3b, p4a, p4b)

Sample Quiz: (Interactive, PDF)

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Unit 3-6: Intercept Form of a Parabola (Doc, PDF, Key)
Georgia Standards of Excellence (Click to Expand)
MGSE9-12.A.SSE.3a: Factor any quadratic expression to reveal the zeros of the function defined by the expression.

MGSE9-12.F.IF.2: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

MGSE9-12.F.IF.7: Graph functions expressed algebraically and show key features of the graph both by hand and by using technology.

MGSE9-12.F.IF.7a: Graph quadratic functions and show intercepts, maxima, and minima (as determined by the function or by context).


MGSE9-12.F.IF.8: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
Video Lessons: (p1, p2)

Sample Quiz: (Interactive, PDF)

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Unit 3-7: Function Model Comparisons (Doc, PDF, Key)
Georgia Standards of Excellence (Click to Expand)
MGSE9-12.F.IF.4 Using tables, graphs, and verbal descriptions, interpret the key characteristics of a function which models the relationship between two quantities. Sketch a graph showing key features including: intercepts; interval where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.

MGSE9-12.F.IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.
Video Lessons: (p1, p2, p3)

Sample Quiz: (Interactive, PDF)
3-09
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