In this lesson, students use the process of completing the square to rewrite quadratic expressions from standard form to vertex form. Then, they determine whether two functions are equivalent by asking a partner for unknown information.

The lesson begins with a review of vertex form, its advantage, and its connections to the graph. Then, students recall how to transform expressions in vertex form into standard form and experiment with transforming the same expressions back to vertex form. Students notice that to take an expression from standard form to vertex form is essentially to complete the square while being careful not to change the value of the expression.

An optional activity in which students do the same process with a leading coefficient other than 1 is included. If students move quickly through the process of converting to vertex form or are curious about how to work with these other expressions, consider making time for the activity.

To transform expressions into vertex form, students need to look for and make use of structure (MP7). As students ask for information using the Information Gap routine, they must be precise in their language and questioning (MP6).