##
* *Reflection: Student Ownership
Different Forms of Quadratic Functions - Section 2: Investigation and New Learning

Something that I really enjoyed about this lesson was the opportunity for students to use technology to check their own answers. Basically, they could come up with the equation that they thought was equivalent, and then graph this equation along with the original equation and see if the graphs were the same. This was really empowering for students, from struggling students to high performing students. I found for struggling students that it gave them a starting point--even if they couldn't come up with an algebraic method to convert the equations to different forms, they could basically guess and check until something worked. I encouraged them to ask me this question: "I found the right answer by playing around with the graph, but could you show me how to find this answer using algebra?" I wrote this question on the board, and told students to ask me whenever they wanted, and I would should this. This was incredibly empowering for them, because it showed them that I thought it was totally okay to play around on the computer, but also that there is more than one way. Some students were more reluctant to learn the algebra, so I told them I eventually wanted them to be able to find the equivalent expressions without a computer, but they didn't have to learn that today. Having the graphing technology available basically gave students the chance to learn the algebra when they were ready and wanted to do so. It also made it much easier for me to manage the class, because students weren't begging me to check their answers. This freed me up to focus on helping smaller groups of students learn or review the algebraic strategies when they asked me to show them.

*Students Check their Own Answers with Technology*

*Student Ownership: Students Check their Own Answers with Technology*

# Different Forms of Quadratic Functions

Lesson 11 of 17

## Objective: SWBAT develop methods to write quadratic functions in standard, vertex and factored form.

## Big Idea: How can we write quadratic functions in different ways? What does each form of a quadratic function tell us about the graph of the function?

*70 minutes*

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- UNIT 1: Linear and Nonlinear Functions
- UNIT 2: Piecewise Functions
- UNIT 3: Absolute Value Functions and More Piecewise Functions
- UNIT 4: Introduction to Quadratic Functions through Applications
- UNIT 5: More Abstract Work with Quadratic Functions
- UNIT 6: Rational Functions
- UNIT 7: Polynomial Functions
- UNIT 8: Exponential Functions
- UNIT 9: Ferris Wheels
- UNIT 10: Circles
- UNIT 11: Radical Functions
- UNIT 12: Cubic Functions

- LESSON 1: Investigating Profit with Products
- LESSON 2: More Profit Maximization Investigations
- LESSON 3: Profit Maximization Problems Workshop: Multiple Methods
- LESSON 4: Multiple Methods to Solve Problems with Quadratic Functions
- LESSON 5: More Multiple Methods to Solve Problems involving Quadratic Functions
- LESSON 6: 4-Column Quadratic Data Tables
- LESSON 7: More 4-Column Data Tables
- LESSON 8: Applying Data Tables to Word Problems
- LESSON 9: Profit Maximization and 4-Column Data Tables Review
- LESSON 10: Profit Maximization and 4-Column Data Tables Summative Assessment
- LESSON 11: Different Forms of Quadratic Functions
- LESSON 12: Quadratic Data Tables
- LESSON 13: Finding Vertices of Parabolas
- LESSON 14: Heights of Falling Objects
- LESSON 15: Profit Maximization
- LESSON 16: Quadratic Functions Review and Portfolio
- LESSON 17: Quadratic Functions Summative Assessment