Algebra Homework Should Not Interfere With College Football

I was watching a college football game on TV this past Saturday when I heard my spouse growling profanities under her breath.  It seems she was trying to complete an algebra test, but some of the questions were giving her fits.  I happened to glance her way during one of her profane outbursts and saw the following question in contained in the examination.

(Actual question in my spouse's algebra test)


For each function find:
a. the maximum number of real zeros that the function can have
b. the maximum number of X-intercepts that the graph can have
c. the maximum number of turning points that the graph can have

So I thought I would try my hand at answering it. (Quiet the laughter, Please!). Well, I skipped part A right off the bat, but don't worry, I will return to it.

Now on to part B. That one was easy. The maximum number of possible X-intercepts equals the number of times Y throws the football.

Part C was easy too. Turning points? For a graph? Right....only people  and football games have turning points.

Now, for part A - the maximum number of REAL zeros that the function can have(?).

The first thing that crossed my mind was...what, there are IMAGINARY zeros?! Guess what! It turns out that, YES, there REALLY ARE IMAGINARY ZEROS, and they are not figments of mathematicians' imagination. (Right!) Now, if you dispute the possibility of the existence of IMAGINARY ZEROS, you will merely flunk algebra. But if you try to convince people that there are space aliens living among us, that Big Foot is in love with Chupakabra, etc., the same mathematician that created the IMAGINARY ZERO will call YOU crazy. What a strange world we live in!

Incidentally, when I checked my answers in the "back of the book" I found that the editors had made some mistakes.  None of the provided answers matched my own.  Apparently the authors of the algebra text believe that the answers to the above problem are expressed "mathematically" through the long and tedious process known as "working out" the problem. 

I totally disagree with the provided answers.  Not only are my answers simpler and more straightforward, they close the mathematics discussion rather quickly.  This allows me to get back to my favorite Saturday afternoon  pass time: watching college football.  Oh look, Y threw ANOTHER X-intercept! Go Raiders!!



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