Math Arguments

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

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Item 190

Which values of x do we choose? Conics

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?


\(x^2+y^2=25\)

\(\dfrac{(x-1)^2}{9}+\dfrac{(y+2)^2}{16} = 1\)

\(\dfrac{(x-4)^2}{9}-\dfrac{(y-4)^2}{16} = 1\)


What are your favorite examples of this?


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Smart Substitution
T.R.Milne
PRE-CALC

Source: T.R.Milne
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