Math Arguments

Problems, Questions, and Puzzles to spark discussion and argument in the maths classroom.

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Item 216

Which values of x do we choose? Polynomials

For the following functions, think about "How to graph like a math teacher." Math teachers want to sketch graphs quickly and efficiently and choose values of x that work "nicely" in the equation and  generate integer values of y, thus making it easier to graph.

Which points in the graph:
- are best found by inspection?
- are best found by substitution?
- are best found by symmetry?

\(y = (x-2)^2(x+2)\)

\(y = (x-1)^3\)

\(y = x^3-8\)

\(y=x^3+3x^2\)

\(y=(x-3)^2(x+3)^2\)


What are your favorite examples of this?


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Smart Substitution
T.R.Milne
ALG2

Source: T.R.Milne
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