Students will exploring how chaning the equation of a parabola on Desmos.com will give you similar graphs. These equations are all in vertex form and will ask students to determine the vertex of each equation. Students will all be asked to graph each of the equations in the families as well. Original worksheet created by Curt Sauer.

This task shows three equivalent expressions and requires that students understand the structure and purpose of each one. This is a critical aspect of Seeing Structure in Expressions. 
The primary purpose of this task is to assess students' knowledge of certain aspects of the mathematics described in the High School domain A-SSE: Seeing Structure in Expressions. Specifically, standard A-SSE.3 reads A-SSE.3: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. a. Factor a quadratic expression to reveal the zeros of the function it defines. b. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.
The Standards avoid the term "simplify" as there isn't always an obvious simplest form. The emphasis instead is on, "purposeful transformation of expressions into equivalent forms that are suitable for the purpose at hand." This task shows three equivalent expressions and requires that students understand the structure and purpose of each one. This is a critical aspect of Seeing Structure in Expressions. 
Mathematically this task:
• Prompts students to analyze three equivalent quadratic expressions • Allows students to focus on the structure of the expressions without focusing on the procedural skill of factoring or expanding the expressions • Gives a real-world context for students to interpret the properties of quadratic expressions • Requires students to look for and make use of structure (MP.7)
In the classroom: • Offers students and teachers an opportunity to see an assessment-type task with two response types • Allows teachers to target specific student misunderstandings for reteaching • With follow-up questions, teachers can prompt students to share their thinking about the concepts in this task