Module 1b - Quadratic Functions

October 5 - November 7

Students will:

• Analyze a real world situation where the rate of change is not constant.

• Identify and interpret key features of a quadratic that represent a real world context.

• Use vertex form of a quadratic in order to create a graph and vice versa.  

• Interpret key features of a graph.

• Use vertex form of a quadratic equation in order to create a graph and vice versa.  

• Use the discriminant to determine the nature of solutions of quadratics.

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October 6 - Introduction to Quadratic Functions

Students learned how to recognize a quadratic function and to label and find the key parts of the graph.

Vertex, maximum, minimum, solutions, axis of symmetry.

Labeling a parabola (video lesson)

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Algebranation.com  Section 6: Quadratic Functions, part 1

Sign in with Bartow Senior High.

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October 9 - Multiplying Binomials.  This is a review in preparation for factoring.

Kahn Academy lesson

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Math Bits Notebook:  Methods for multiplying binomials

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October 13 - Factoring quadratic expressions using the Area Model (Box)

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Video using area model to factor  (this is the box)

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October 17 - Factoring quadratic expressions using the grouping method

Video using grouping to factor

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 October 24 - Using the Zero Product Property to find the Solutions.

 Watch how we can solve equations using this property.

Algebra Nation, Section 2, Topic 4

October 30 - Factoring Special Cases.  Tips and tricks.  Putting quadratics in standard form.

Remember, the area model methods and grouping methods that were taught can be used to factor all quadratics.  You must make sure that you choose the correct a, b, and c.  If there is no b or c present, then they will be equal to zero.  Shortcuts are always helpful in math though!  

Watch here to see a video about some special cases.

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To work with quadratics we must first put them in standard form.  If we don't, we will likely use the wrong numbers for our a, b, or c.  

Watch here to learn how to do this.

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November 1 - Solving Quadratic Application word problems

Here is a good example like we did in class.

Some reading and other samples.

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November 3 - Solving Quadratics by Completing the Square

Watch here to see an example.

Read the steps you need to do to complete the process.

This is a good description along with a video.

Practice problems.

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I will give 25 points extra credit for the first person to tell me that this offer is here.

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November 9 - the Quadratic Formula

Watch some examples.

Here is the song!  Write and video your own song for extra credit!

Read about it.

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November 14 - the Discriminant

Learn about the discriminant

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Welcome back from Thanksgiving Break.  We will be working with quadratics through the end of this year.  We will be graphing them, primarily.

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November 27 - Quadratics in Action.

Algebra Nation Section 5, Topic 10.

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November 29 - Observations from graphing a quadratic function.

Algebra Nation Section 6, Topic 1

Watch this nice lady on youtube. :)

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December 1 - Graphing Quadratics using a table

Algebra Nation - Section 6, Topic 3

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December 5 - Graphing Quadratics by finding the axis of symmetry and vertex

How to find the axis of symmetry 

How to find the axis of symmetry and use that to find the vertex.  Good lesson.

Here is a good written lesson about all things parabola, including when the graph opens up or down.

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        MAFS.912.F-IF.2.4: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.

        MAFS.912.A-REI.2.4: Solve quadratic equations in one variable. b. Solve quadratic equations by inspection (e.g., for x² = 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.

        MAFS.912.A-SSE.2.3: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. ★ a. Factor a quadratic expression to reveal the zeros of the function it defines. b. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.

        MAFS.912.F-IF.3.8: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. a. 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.

        MAFS.912.A-CED.1.2: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

Students will:

• Factor quadratic expressions using various methods.

• Find the zeros of a quadratic equation and use the zero product property to determine the solutions.

•  Factor quadratics not in standard form and with leading coefficients not equal to one.

• Factor using perfect square trinomials and difference of squares.  

• Solve quadratic equations by taking square roots.

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Algebranation.com  Section 5: Quadratic Functions, part 1

Sign in with Bartow High School.

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        MAFS.912.A-SSE.2.3: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. ★ a. Factor a quadratic expression to reveal the zeros of the function it defines.

         MAFS.912.A-SSE.1.2: Use the structure of an expression to identify ways to rewrite it. For example, see x4 - y 4 as (x²)² – (y²)², thus recognizing it as a difference of squares that can be factored as (x² – y²)(x² + y²).

        MAFS.912.A-REI.2.4: Solve quadratic equations in one variable. b. Solve quadratic equations by inspection (e.g., for x² = 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.