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- HSA-REI.B.4aUse the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)<sup>2</sup> = q that has the same solutions. Derive the quadratic formula from this form.
- HSA-REI.B.4bSolve quadratic equations by inspection (e.g., for x<sup>2</sup> = 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.

Three Methods of Solving Quadratics and Word Problems

Algebra I

» Unit:

Quadratic Functions

Big Idea:The structure of a quadratic equation can help students determine how to solve the equation.

Moving Toward Mastery: Completing the Square (Day 1)

Algebra I

» Unit:

Quadratic Functions

Big Idea:There are uses for completing the square: first, as it relates to vertex form and graphing parabolas, and second as it relates to solving quadratic equations. Today, we'll get at both.

Moving Toward Mastery: Completing the Square (Day 2)

Algebra I

» Unit:

Quadratic Functions

Big Idea:Students will continue to see that graphing quadratic equations and solving them work in tandem: the better we understand one, the more sense the other will make!

Quadratic Functions in Three Forms

Algebra I

» Unit:

Quadratic Functions

Big Idea:An brief adventure in number theory provides some background knowledge for completing the square, then students get to practice manipulating quadratic expressions in different forms.

Building Quadratic Functions: f(x), kf(x) and f(kx)

Algebra I

» Unit:

Interpret and Build Quadratic Functions and Equations

Big Idea:Students use technology to construct their own understanding of different operations on the graph of quadratic functions!

Irrational Zeros of Quadratic Functions

Algebra I

» Unit:

Quadratic Functions

Big Idea:This lesson allows students to connect the graphical and algebraic representation of irrational roots of a quadratic function.

Performance Task: Pulling It Together with Quadratics

Algebra I

» Unit:

Interpret and Build Quadratic Functions and Equations

Big Idea:Students integrate concepts learned about quadratic equations and functions to analyze models and make recommendations for maximizing profit on the sale of smart phones.

Unit Assessment: Quadratic Functions and Equations

Algebra I

» Unit:

Interpret and Build Quadratic Functions and Equations

Big Idea:Students complete a unit assessment aligned to unit standards - provides excellent data source for teacher's to adjust and refine their curriculum and instruction!

Quadratic Function Jigsaw

12th Grade Math

» Unit:

Polynomial and Rational Functions

Big Idea:Use a jigsaw grouping technique to review quadratic functions.

Quadratic Equations, Day 2 of 2

Algebra II

» Unit:

The Complex Number System

Big Idea:Knowledge of quadratic equations is an important prerequisite for studying complex numbers.

Factoring and Completing the Square to Find Zeros

Algebra I

» Unit:

Interpret and Build Quadratic Functions and Equations

Big Idea:Quadratic expressions are reformatted by integrating background knowledge in factoring polynomials and graphing functions!

The Three Musketeers: Simplifying the Quadratic Formula

Algebra I

» Unit:

Interpret and Build Quadratic Functions and Equations

Big Idea:Just like the Three Musketeers, the three pieces of the quadratic formula stick together, and work together to find solutions!

Quadratic Quandaries: Modeling with Quadratic Functions

Algebra I

» Unit:

Interpret and Build Quadratic Functions and Equations

Big Idea:Students complete a number of application problems related to quadratic functions and create their own Quadratic Quandary!

Quadratic Functions: Vertex Form

Algebra II

» Unit:

Polynomial Functions and Expressions

Big Idea:Quadratic functions are graphed as parabolas; how we go about creating the graph depends on which form the function is written in.

Polynomial Function Workshop

12th Grade Math

» Unit:

Polynomial and Rational Functions

Big Idea:Take a breather and summarize the important concepts involving polynomial functions.

HSA-REI.B.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.

HSA-REI.B.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.