Unit 5: Quadratic Functions and Transformations
Lesson Video
Focus Standards
Learning Focus
Additional Resources
A Develop Understanding Task
Reviews the use of quadratic and linear functions for modeling geometric patterns.
- How can I use representations to model a growing pattern?
- What kind of function is the sum of a linear and quadratic function?
A Develop Understanding Task
Reviews using quadratic functions to model area and identifying features of quadratic functions such as domain, range, and intervals of increase and decrease.
NC.M2.A-CED.2
NC.M2.A-SSE.1
NC.M2.A-SSE.1.a
NC.M2.A-SSE.1.b
NC.M2.F-BF.1
NC.M2.F-IF.4
NC.M2.F-IF.7
Model a story context with a table, graph, and equation.
Identify features of a function from a graph.
Why are quadratic equations often used to model area?
Lesson 3: Well, What Do You Know?
A Develop Understanding Task
Reviews factoring and using factored form of a quadratic function to identify the vertex and line of symmetry and graph a parabola.
Use patterns to efficiently graph quadratic functions from factored form.
How does the graph of a parabola relate to the equation of a quadratic function?
What features of a parabola are highlighted in factored form? How can we use those features to graph a quadratic function?
A Develop Understanding Task
Surfaces thinking about transforming quadratic function by comparing f(x) with transformed functions, such as f(x) + 5, f(x + 5), 5f(x), f(5x).
Find patterns in the equations and graphs of quadratic functions.
What happens to the graph of f(x) =x^2 when the equation is changed by adding, subtracting, or multiplying by a constant?
A Solidify Understanding Task
Solidifies understanding of transformations of quadratic functions, as students write and graph quadratics with multiple transformations.
Write equations for functions that are transformations of f(x) = x^2.
Find efficient methods for graphing transformations of f(x) = x^2.
What happens to the graph of f(x) = x^2 when more than one transformation is applied?
A Develop Understanding Task
Introduces the procedures for squaring a binomial and completing the square for ax^2 + bx + c with a = 1, and b, c> 0 , using area models that represent the Distributive Property.
Find the square of a binomial expression.
Recognize a perfect square trinomial.
Create perfect squares from partial areas.
Find relationships between terms in a perfect square trinomial.
How can we use models to find equivalent expressions for perfect squares?
A Solidify Understanding Task
Extends understanding of how to complete the square with area models, to include quadratic expressions with a does not equal 1 and trinomials that are not perfect squares.
Find a process for completing the square that works on all quadratic functions.
Adapt diagrams to become more efficient in completing the square.
How can we complete the square when there is more than one square given (or a is not equal to 1 in ax^2 + bx + c) ?
A Practice Understanding Task
Connects graphing a parabola in vertex form to completing the square.
Use completing the square to change the form of a quadratic equation.
Graph quadratic equations given in standard form.
How might completing the square help us to graph parabolas?
Alternative method: Video 1: Factoring Using the box method,
A Practice Understanding Task
Builds fluency in writing and connecting different forms of a quadratic function, using factoring, completing the square, and the distributive property. Connects different forms of quadratics to their graphs.
Choose the most efficient form of a quadratic function.
Become efficient and accurate in converting from one quadratic form to another.
Become efficient and accurate in identifying features of the graph of quadratic functions from a given form.
What information do we get from each form of a quadratic equation, and which form is best for a particular purpose?