HSA-REI.B.4a
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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)^{2} = 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^{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.
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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.
23 Lesson(s)
Three Methods of Solving Quadratics and Word Problems
Algebra I »
Unit: Quadratic Functions
Algebra I »
Unit: Quadratic Functions
Big Idea:
The structure of a quadratic equation can help students determine how to solve the equation.
Standards:
Favorites
(5)
Resources
(15)
Reflections
(1)
Moving Toward Mastery: Completing the Square (Day 1)
Algebra I »
Unit: Quadratic Functions
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.
Standards:
Favorites
(2)
Resources
(28)
Reflections
(1)
Moving Toward Mastery: Completing the Square (Day 2)
Algebra I »
Unit: Quadratic Functions
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!
Standards:
Favorites
(1)
Resources
(15)
Reflections
(1)
Quadratic Functions in Three Forms
Algebra I »
Unit: Quadratic Functions
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.
Standards:
Favorites
(7)
Resources
(24)
Reflections
(3)
Building Quadratic Functions: f(x), kf(x) and f(kx)
Algebra I »
Unit: Interpret and Build Quadratic Functions and Equations
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!
Standards:
Favorites
(1)
Resources
(19)
Reflections
(1)
Irrational Zeros of Quadratic Functions
Algebra I »
Unit: 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.
Standards:
Favorites
(1)
Resources
(14)
Reflections
(1)
Performance Task: Pulling It Together with Quadratics
Algebra I »
Unit: Interpret and Build Quadratic Functions and Equations
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.
Standards:
Favorites
(13)
Resources
(10)
Unit Assessment: Quadratic Functions and Equations
Algebra I »
Unit: Interpret and Build 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!
Standards:
Favorites
(23)
Resources
(6)
Quadratic Function Jigsaw
12th Grade Math »
Unit: Polynomial and Rational Functions
12th Grade Math »
Unit: Polynomial and Rational Functions
Big Idea:
Use a jigsaw grouping technique to review quadratic functions.
Standards:
Favorites
(3)
Resources
(16)
Quadratic Equations, Day 2 of 2
Algebra II »
Unit: The Complex Number System
Algebra II »
Unit: The Complex Number System
Big Idea:
Knowledge of quadratic equations is an important prerequisite for studying complex numbers.
Standards:
Favorites
(3)
Resources
(19)
Reflections
(1)
The Three Musketeers: Simplifying the Quadratic Formula
Algebra I »
Unit: Interpret and Build Quadratic Functions and Equations
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!
Standards:
Favorites
(7)
Resources
(17)
Reflections
(1)
Quadratic Quandaries: Modeling with Quadratic Functions
Algebra I »
Unit: Interpret and Build Quadratic Functions and Equations
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!
Standards:
Favorites
(5)
Resources
(26)
Reflections
(3)
Factoring and Completing the Square to Find Zeros
Algebra I »
Unit: Interpret and Build Quadratic Functions and Equations
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!
Standards:
Favorites
(3)
Resources
(19)
Reflections
(1)
Quadratic Functions: Vertex Form
Algebra II »
Unit: Polynomial Functions and Expressions
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.
Standards:
Favorites
(3)
Resources
(22)
Reflections
(1)
Polynomial Function Workshop
12th Grade Math »
Unit: Polynomial and Rational Functions
12th Grade Math »
Unit: Polynomial and Rational Functions
Big Idea:
Take a breather and summarize the important concepts involving polynomial functions.
Standards:
Favorites
(7)
Resources
(7)
Reflections
(1)
Common Core Math
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