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Put the Variable in Parentheses


Date: 10/15/2001 at 07:39:38
From: John Greaney
Subject: Quadratic functions plotting the parabola

For the equation y = x^2 + x - 6  range -4 to 3 I get the following 
coordinates:

             x -4  -3  -2  -1  0  1  2  3                             
             y -26 -18 -12 -9 -6 -4  0  6  
                           
The answers and the graph in my book look totally different.        

Here is some of my working out:

   x= -4 therefore  -4 sqd-4-6 = -16-4-6 = -26 

Am I on the right track? 
 
Thanks, John


Date: 10/15/2001 at 12:52:01
From: Doctor Peterson
Subject: Re: Quadratic functions plotting the parabola

Hi, John.

Be careful multiplying negative numbers! Remember that the square of 
-4 is -4 * -4, which is the positive number 16, not -16.

Perhaps you confusing yourself by writing the expression down without 
thinking about the order of operations. You need to write

        2
    (-4)  + (-4) - 6 = 16 - 4 - 6 = 6

If you wrote

      2
    -4  + -4 - 6 = -16 - 4 - 6 = -26

you did not write what you really meant, because this says to square 4 
and then take the negative of the result, which is different from 
squaring -4.

I recommend always putting the value of the variable in parentheses, 
to ensure that it is kept together when you evaluate it, rather than 
ripping the minus sign off as you did.

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/   
    
Associated Topics:
High School Negative Numbers
Middle School Negative Numbers

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