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Whats up with spacing of x^2, 0.5x^2, and 2x^2!?

So, I was playing with an online graphing calculator and I plugged in 0.5xxand 2xand when I went up to higher numbers, such as x=10, I noticed they were unevenly spaced. This puzzles me because 0.5xand 2xSHOULD be equally spaced from xbecause they are both off by a factor of 2, but 0.5xis farther away from xthan 2xis. :O
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2 Answers

Actually, the only point where 0.5x2 and 2x2 are evenly spaced from x2 is at x = 0.

This is found by taking the difference between x2 and the other equation at any given point
|2x2 - x2| and |0.5x2 - x2|

And then setting them equal to each other.
|2x2 - x2| = |0.5x2 - x2| → x2 = 0.5x2 → x = 0.5x
 
But that isn't your question. Numbers always have patterns, so let's see if we can find this one. :)
Using the same functions, we can make a table to look at how things are spaced. I'll be going up in increments of 1, starting at 0.

0.5x2 | x2 | 2x2 | 2x2 - x2 | x2 - 0.5x2
0       | 0   | 0    | 0            | 0
0.5    | 1   | 2     | 1           | 0.5
2       | 4   | 8    | 4            | 2
4.5    | 9   | 18   | 9           | 4.5
8       | 16 | 32   | 16          | 8
 
So there's our pattern. Comparing just the last two columns, we see that for each increment the difference is doubled. This makes sense because the difference between 2x2 and x2 is twice as large as the difference between 0.5x2 and x2.

I hope that helped!
 

Comments

The coefficient in front of the x squared causes the graph to change the width of the graph.
The coefficient of 1 is the basic x squared function.  If the coefficient is above 1, then the graph will rise faster and be narrowed.  If the coefficient is less than 1 then the graph will rise slower and thus be a wider graph.   foe instance  if x is 3, then x^2 = 9,  .5 * x^2 = 4.5, and  2 * x^2 = 18.
If you have a graphing calculator, use the Table (2nd Graph) to see all three functions compared for each value of x.
Hope this is helpful.
 

Comments