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Section: A1.7.4

Put quadratic functions in vertex form

Put quadratic functions in vertex form (A-SSE.B.3b$^\star$, F-IF.C.8a$^\star$).

In this section, students adapt the method of completing the square from solving quadratic equations to putting into vertex form the expressions that define quadratic functions. This connects with the work in the Quadratic Functions unit Section 7, where students saw the geometric meaning of vertex form but did not necessarily learn how to put a quadratic function in that form.

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Tasks

1 Identifying Quadratic Functions (Standard Form)

WHAT: Students are given graphs of quadratic functions and must find expressions for them. There are many possible solution methods; the one given uses vertex form.

WHY: In preparation for the general method of putting a function in vertex from by completing the square, this activity reminds students of the relationship between that form and the graph of the function.

2 Rewriting a Quadratic Expression

WHAT: Through a scaffolded series of questions, students convert expressions in standard form to vertex form in order to find their maximum and minimum values (MP7).

WHY: The goal of this task is to show how completing the square in a quadratic expression can reveal minimum or maximum values of the function defined by the expression.