Unit 7: Structures of Quadratic Expressions
Lessons
Focus Standards
Learning Focus
Additional Resources
Lesson 1: Quick It's Quadratic
A Develop Understanding Task
Explores the use of the standard form of a quadratic function to identify features of the graph without formulas for finding the vertex or line of symmetry.
Find patterns in the equations and graphs of quadratic functions.
How can the graph of a quadratic function be predicted from the equation?
Lesson 2: Adding Your Two Cents
A Develop Understanding Task
Introduces algebraic and graphical methods for adding and subtracting quadratic functions. Relates the structure of quadratic polynomials to whole numbers.
Add and subtract linear and quadratic functions algebraically.
Add and subtract linear and quadratic functions graphically.
How are quadratic expressions like whole numbers?
How is adding and subtracting whole numbers like adding and subtracting quadratic expressions? How is it different?
Lesson 3: Factor Fixin
A Solidify Understanding Task
Introduces the concept of factoring trinomials and the concept of multiplying two binomials using area models and the distributive property to show that factored and standard forms of a quadratic expression are equivalent. Develops the relationship between b and c in a factorable trinomial.
Multiply two binomials using diagrams.
Factor a trinomial using diagrams.
How can we use diagrams to write equivalent expressions for the area of a rectangle?
Lesson 4: The x-Factor
A Solidify Understanding Task
Connects standard and factored forms of quadratic equations, where a=1, but b and c can be positive or negative.
Find patterns in signs and numbers to help factor and multiply expressions.
Use area model diagrams to multiply binomials with different signs.
Use area model diagrams to factor trinomials when some of the terms are negative.
What happens to the factors of a quadratic expression when some of the terms are negative?
Lesson 5: The Wow Factor
A Solidify Understanding Task
Connects the factored and expanded form of a quadratic. Builds fluency and efficiency when considering factors of a in combination with factors of c.
Use diagrams to factor trinomial expressions when the leading coefficient is not 1.
How can we factor ax^2+bx+c when a does not equal 1?
Lesson 6: Stretching My Quads
A Practice Understanding Task
Relates features of the graph of a quadratic function that can be seen in the equation written in factored form, including x-intercepts, line of symmetry, and vertex. Connects finding x-intercepts of a quadratic function to finding the solutions of a quadratic equation in factored form.
Find patterns to efficiently graph quadratic functions from factored form.
What features of a parabola are highlighted in factored form? How can we use those features to graph a quadratic function?
How does factored form of a quadratic equation relate to solving quadratic equations?
Lesson 7: Taking the Scenic Root
A Develop Understanding Task
Introduces solving quadratic equations graphically and using inverse operations, including taking the square root of both sides.
Solve quadratic equations graphically and algebraically.
Make connections between solving quadratic equations and graphing quadratic functions.
How can we solve quadratic equations that can’t be factored easily?
How can we use graphs to solve quadratic equations?
Lesson 8: Quadratic Quarters
A Practice Understanding Task
Develops fluency in solving quadratic equations by factoring or using inverse operations. Builds fluency in relating equations and graphs of quadratic functions.
NC.M1.A-APR.1
NC.M1.A-APR.3
NC.M1.A-REI.1
NC.M1.A-REI.4
NC.M1.A-SSE.3
NC.M1.F-IF.4
Solve quadratic equations efficiently and accurately.
Identify information about the graph of a quadratic function from the equation.
What information do we get from each form of a quadratic equation, and which form is best for a particular purpose?
How can you determine the most efficient strategy for solving any particular quadratic equation?