Higher-degree polynomials (end behavior, zeros, multiplicity)
Teacher tools for this standard
Lesson Plan · Guided Notes · Exit Ticket · Re-teach · Homework
Teacher tools for this standard
Lesson Plan · Guided Notes · Exit Ticket · Re-teach · Homework
- Lesson Plan →Objectives, pacing and practice, built from this lesson's brief.
- Guided Notes →One page your students fill in and keep.
- Exit Ticket →Three items at the end of class. No student accounts.
- Re-teach →After an exit ticket: who missed what, and what to do tomorrow.
- Homework →Assign practice; it grades itself.
"Make connections between a table, an algebraic representation, or a graph of a: • polynomial function, simple rational function, or quadratic or exponential function that involves a transformation, not in context."
"Make connections between a table, an algebraic representation, or a graph of a: • polynomial function, simple rational function, or other nonlinear function in a context, or a quadratic or exponential function that involves a transformation in a context."
"Understand and use the fact that for the graph of y = f ( x ), the solutions to f ( x ) = 0 correspond to x-intercepts of the graph and f (0) corresponds to the y-intercept of the graph; make connections between the input/output pairs and points on a graph; interpret this information in a context."
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"Make connections between a table, an algebraic representation, or a graph of a: • polynomial function, simple rational function, or quadratic or exponential function that involves a transformation, not in context."
"Make connections between a table, an algebraic representation, or a graph of a: • polynomial function, simple rational function, or other nonlinear function in a context, or a quadratic or exponential function that involves a transformation in a context."
"Understand and use the fact that for the graph of y = f ( x ), the solutions to f ( x ) = 0 correspond to x-intercepts of the graph and f (0) corresponds to the y-intercept of the graph; make connections between the input/output pairs and points on a graph; interpret this information in a context."
What you'll learn
- Sketch a polynomial from its factored form, and match it to a graph or a table, using four facts: degree, leading-coefficient sign, zeros with multiplicities, and the y-intercept
- Determine both ends' behavior from degree parity and leading-coefficient sign, and explain why the leading term decides the ends
- Find all real zeros of a polynomial in factored form, state each zero's multiplicity, and predict crossing or touching with a sign test
- State the maximum number of real zeros and turning points a degree-n polynomial can have
- Locate a zero in a table of values by a sign change between rows
Slides
Step through the lesson, or watch it as a narrated video
Slides
In development
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