329: 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 are best found by inspection?
• Which points are best found by substitution?
• Which points 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?