# Daily Desmos 44b (Grunnleggende, which is Norweigian for "Basic")

## Creator

Michael Pershan (@mpershan )

## Difficulty

Basicish

## On to the Challenge!

OK, here’s the deal. One of these graphs is quadratic, and the other is exponential. Which one is which, and how do you know? Go to desmos.com and try it out.

https://www.desmos.com/calculator/rw1mi0qakl

We made this graph by starting out with two equations y=2^x and y=x^2. We then added different elements to the equation until it fit this graph. So the orange one is exponential and the black one is quadratic.

In the corner of the picture, it looks like the black one is flat, going to go back up, and the orange one looks like it is going to continue sloping down. So, we started with the equation y=2^x for the orange one and y=x^2 for the black one, guessing that the orange is exponential and the black is quadratic (because of the way the corner looked). Both go through the origin so we subtracted one from the exponential equation (y=(2^x)-1). We also saw that the exponential equation looked like it went through the point (6,2), so we tried multiplying x in that equation by different numbers (starting using the slider on desmos) and we got the exponential equation y=(2^.265x)-1 and it matched up with the black line in the picture. We then tried to make y=x^2 wider to go through the point (5,.25) and ended up with the equation y=.05x^2. Both these equations match pretty well with the picture.

https://www.desmos.com/calculator/dwcnwcdlr9

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