Math
posted by CC .
13. Find the vertex of the parabola.
y = 2x2 + 12x  13
(5, 3)
(3, 5)
(3, 5)
(5, 3)

y = 2x^2 + 12x  13
there are many ways to determine the vertex, but the easiest (for me) i think is to use derivatives. first we get the derivative with respect to x:
y = 2x^2 + 12x  13
y' = 4x + 12
then we equate this to zero (because vertex is a maximum or a minimum and therefore the slope is zero):
0 = 4x + 12
4x = 12
x = 3
substitute this back to the original given equation:
y = 2x^2 + 12x  13
y = 2(3^2) + 12(3)  13
y = 18 + 36  13
y = 5
therefore vertex is at
(3, 5)
hope this helps~ :) 
As always, love your comrentamy on the world around us.I do have a quick rationale for why the bold 'Contains peanuts', though.It's somewhere at the intersection of allergies and the covering our buttness of most companies.Anything that can be potentially allergyinducing (peanuts, soy, wheat, milk, and I am sure that list will only get longer) seems to now be showing up in bold at the bottom of ingredient lists. On one hand this is a good thing for those parents who need to scan each label attached to the foods they buy for allergic kids. Sometimes the lists are akin to Russian literature and this saves time (though most parents I know read the list anyways, so this part of the rationale is somewhat moot). On the other hand, this is a way for companies to ward off litigious consumers. Remember the somewhere close to 3 million (that's dollars!) reasons McDonald's paper coffee cups have 'warning, contents are hot' signs on them?And that pretty much gets us back to your original theory  do we really have a hope to teach advanced learning theories to a society that doesn't recognize that coffee is hot and peanuts contain peanuts? Or could it be that people do know this but will do pretty much anything to make a buck?
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