F-IF.3.8.a

Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

a. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.

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Formative Assessments
Formative Assessments
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Students are asked to rewrite a quadratic function in an equivalent form by completing the square and to use this form to identify the vertex of the graph and explain its meaning in context.
A Home for Fido
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Students are asked to factor and find the zeros of a polynomial function given in context.
Launch From a Hill
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Virtual/Hands-on Manipulatives
Virtual/Hands-on Manipulatives
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Assessment Questions
Assessment Questions
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Videos of Expert Instruction
Videos of Expert Instruction
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This video gives a more in-depth look at graphing quadratic functions than previously offered in Quadratic Functions 1.
Quadratic Functions 2
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This video will demonstrate how to solve a quadratic equation using square roots.
Solving Quadratic Equations using Square Roots
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Hook/Performance Tasks
Hook/Performance Tasks
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The problem presents a context where a quadratic function arises. Careful analysis, including graphing of the function, is closely related to the context. The student will gain valuable experience applying the quadratic formula and the exercise also gives a possible implementation of completing the square.
Springboard Dive
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The task addresses knowledge related to interpreting forms of functions derived by factoring or completing the square. It requires students to pay special attention to the information provided by the way the equation is represented as well as the sign of the leading coefficient, which is not written out explicitly, and then to connect this information to the important features of the graph.
Which Function?
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