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Learning Goal
Part of: Analyze functions using different representations — 8 of 10 cluster items
Use factoring and completing the square
HSF.IF.C.8.a
**HSF.IF.C.8.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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HSF.IF.C.8.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.
What you'll learn
- Factor a quadratic function to reveal its zeros and sketch the corresponding x-intercepts on the graph
- Complete the square to rewrite a quadratic in vertex form, revealing the vertex (extreme value) and axis of symmetry
- Identify the axis of symmetry from vertex form as x = h and use it to describe the graph's line of symmetry
- Determine whether the vertex represents a maximum or minimum and interpret this in applied contexts
- Use the zeros and vertex together to describe the complete behavior of a quadratic: where it crosses zero, where it reaches its extreme, and whether it opens up or down
- Interpret factored and vertex forms in real-world contexts, translating algebraic properties into meaningful statements about the situation
Prerequisites
Slides
Interactive presentations perfect for visual learners • In development
Slides
In development
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