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* *Reflection: Coherence
Quadratic Performance Task - Section 2: Explore and Extend

*Sound Algebraic Argument*

*Writing Across the Disciplines: Quadratic Performance Task*

# Quadratic Performance Task

Lesson 10 of 16

## Objective: SWBAT translate from among verbal, numeric, algebraic and graphical representations of quadratic functions.

## Big Idea: Flexibility with quadratic functions is put to the test in this puzzle-like quadratic performance task. Various starting points are provided and the goal is to represent each function in all ways we have studied.

*90 minutes*

#### Warm-Up

*20 min*

As a warm-up, I present students with the x-intercepts (x=3 and x=-1) and y-intercept (y=6) of a quadratic expression and ask them to use the template Warm-Up Quadratic Functions to practice translating the quadratic into its other algebraic forms, graphing, and reporting interesting features of the graph. This warm-up will be challenging for some students because they will be unsure of how to find the value of "a," the coefficient of the squared term. If they are struggling, I remind them that the y-intercept tells them the coordinates of one point on the curve. I make a second copy of this template on the back of the page so that students who complete the exercise quickly can be given a second, more challenging quadratic function to work with. I find that students generally enjoy the puzzle-like aspect of this activity [MP7].

As students complete the warm-up, I check homework with the homework rubric. If there are questions on the homework I will spend a few minutes answering them before we continue our discussion of solving quadratic equations. As always, I try to maximize persistence in homework problems by providing answers on Edmodo and asking students to check their answers before they arrive in class [MP1].

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#### Explore and Extend

*70 min*

In the Quadratic Performance Task, each student is given an 11" by 17" piece of paper with a preprinted 7X7 table. Each row contains various starting points for defining a quadratic function and the student's goal is to provide all missing information about that function (standard form, vertex form, intercepts, graph, etc) [MP6].

- Quadratic Performance Task (Fit to Preview)
- Quadratic Performance Task (Full Size) (Download)

The idea of this task is to give students the opportunity to persist in a challenging task [MP1] and put everything they have learned about quadratic functions together in one activity [MP2, MP7, MP8].

I ask students to complete this activity independently, although I do not mind if they work side-by-side with another student and check in from time-to time. I do not limit graphing calculator use on this activity but I do ask that they make a sound algebraic argument when translating from one form to the other [MP3]. I discuss my expectations for this type of argument in the reflection Sound Algebraic Arguments.

This activity, although very challenging for students, tends to be very popular and a source of pride for students who complete it. This will take at least an hour for most students to complete.

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- LESSON 1: Introduction to Polynomials
- LESSON 2: Seeing Structure in Expressions - Factoring GCF's and Quadratics
- LESSON 3: Connecting Polynomials to Sequences
- LESSON 4: Connecting Polynomials to Geometric Series
- LESSON 5: Quadratic Functions: Standard and Intercept Forms
- LESSON 6: Quadratic Functions: Vertex Form
- LESSON 7: Flexibility with Quadratic Functions
- LESSON 8: Connecting Quadratic Functions and Quadratic Equations
- LESSON 9: Solving Quadratic Equations
- LESSON 10: Quadratic Performance Task
- LESSON 11: Quadratic Modeling (DAY 1)
- LESSON 12: Quadratic Modeling (DAY 2)
- LESSON 13: Quadratic Modeling (DAY 3)
- LESSON 14: Quadratic Modeling (DAY 4)
- LESSON 15: Review Workshop: Polynomial Functions and Expressions
- LESSON 16: Unit Assessment: Polynomial Functions and Expressions