Algebra II: Vertex and Factored Form of Quadratic Functions

Objectives

• Students will be able to identify and justify the effect of changing the parameters of a quadratic function in vertex form and factored form.
• Students will be able to identify and justify the relationship between the factored form and the x-intercepts of the quadratic function.
• Students will be able to identify and justify which form for a quadratic function is more appropriate to use when solving a given problem.

Vocabulary

• factored form of a quadratic function
• vertex
• vertex form of a quadratic function
• x-intercepts (zeroes, roots)

About the Lesson

This lesson involves utilizing sliders on a quadratic function expressed in vertex form and in factored form to determine the effect the parameters have upon the graph of the function.
Students will:

• Manipulate sliders and make and validate conjectures about the relationships between the values of a, h, and k in the equation and the location of the vertex.
• Manipulate sliders and make and validate conjectures about the relationships between the values of a, r, and s in the equation and the location of the zeroes.
• Determine which form of a quadratic function would be most appropriate to solve specific classes of problems.