Math Arguments

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

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Item 189

Which values of x do we choose? Quadratics

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?


\(y = (x+2)(x-4)\)

\(y = -(x+1)(x+5)\)

\(y = x^2 + 6x + 9\)

\(y = \dfrac{1}{4}(x+5)^2\)


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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