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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.

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.

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.

Solving Quadratics by Factoring-Day 1

Algebra I

» Unit:

Quadratic Functions

Big Idea:Factoring can be used as a tool to examine the structure of an equation.

Solving Quadratic Trig Equations (Day 1 of 2)

12th Grade Math

» Unit:

Trigonometric Equations

Big Idea:The class works together to review methods of solving quadratic equations and make connections to quadratic trig equations.

The Pythagorean Theorem and the Distance Formula

Algebra I

» Unit:

Radical Expressions, Equations, and Rational Exponents

Big Idea:The main point of this lesson is for students to recognize the similarities between the Pythagorean Theorem and the Distance Formula.

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!

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!

Puzzling Polynomials and Quizzical Quadratics

12th Grade Math

» Unit:

Polynomial Functions and Equations

Big Idea:Review polynomial operations with NCTM’s polynomial puzzlers and then practice solving quadratic equations by moving through stations.

Quadratic Function Jigsaw

12th Grade Math

» Unit:

Polynomial and Rational Functions

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

The Quadratic Formula-Day 1

Algebra I

» Unit:

Quadratic Functions

Big Idea:Although it is not as efficient as other methods, the quadratic formula can be used to solve any quadratic equation.

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.

Solving Quadratics by Factoring-Day 2

Algebra I

» Unit:

Quadratic Functions

Big Idea:This lesson allows student to get LOTS of algebraic practice while using technology to build conceptual understanding.

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!

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.