Complete the Square (Min, Max)

Examples, solutions, videos, and lessons to help High School students learn to choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

Suggested Learning Targets

Write expressions in equivalent forms by completing the square to convey the vertex form, to find the maximum or minimum value of a quadratic function, and to explain the meaning of the vertex.
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.

Common Core: HSA-SSE.B.3b

Algebra 1 A.SSE.B.3 Complete the Square
Example:
A certain business is marketing its product and has collected data on sales and prices for the past few years. The company determined that when it raised the selling price of the product, the number of sales went down. The cost of producing a single item is $3.00
A) Using the data the company collected in this table, determine a linear expression to represent the quantity sold, Q.
B) Find an expression to represent the profit function, P.

The Max and Min of a Quadratic Function by Completing the Square.

Completing the Square and Vertex Form.

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