Thursday, September 06, 2012

X is for X-Axis

The question was: Which best represents the graph of y = (x-1)(x+4)?



I spend way too much of my time doing stuff like this.  I write and rewrite questions and then send them off with poorly drawn graphs and hope someone with actual ability with computerized graphics can make it look like it should. I send these types of jpgs at least a couple of times a week and every time I do it, I think how much easier it would be to have a fucking scanner. So, I make my (poor attempt at a) drawing, take a picture of it with our digital camera, email it to myself, open it up in Picasa, do whatever I have to do to make it legible, save it to my computer, and then I put it in an email to whoever needs the email.  And then I laugh to myself and say it's better than faxing.  Which is true, but I live in 2012!!  Okay, I'm over it.

Plus, as part of the technology deal at his new school, my husband is getting a scanner.  Thank whatever deity you wish to thank!!

EDITED TO ADD:  Because Elizabeth wanted the answer, here it goes.

So if you have y = (x-1)(x+4), the zeroes, where the graph crosses the x-axis, are located where the y-value is zero.  Any point on the x-axis will be in the form of (x, 0).  So all you need to do is set the equation equal to zero, which is to say, make y = 0.

0 = (x-1)(x+4)

You may remember from third grade the zero product property (ha ha - maybe not).  If you have ab = 0, either a must be 0 or b must be zero because if the product is 0, one of the terms must be zero. If we apply that rule to our equation, then either

x - 1 = 0   OR     x + 4 = 0

Now we solve those with our rusty algebra skillz.  If x - 1 = 0, that makes x = 1. If x + 4 = 0, that makes x = -4.

So we know our graph must cross at (1, 0) and (-4, 0). We can eliminate C & D because the test makers are attempting to confuse us with the wrong signs.  Since parabolas, this type of graph, usually open up, unless it is multiplied by a negative number, we know this one must point up. For example, -1(x-1)(x+4) would be B because the -1 in front would flip the parabola over.  Cross off B. The answer is A.

2 comments:

  1. I want to know the answer!

    ReplyDelete
  2. I almost failed grade 12 math. And that was with 2 hours of tutoring a week!

    ReplyDelete

 
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