Functions in real life

Functions are commonly used in math,science,and engineering.For example,if a bowman wants to shoot an arrow to the target 80 meters away,and the question asks you about the power the bowman should use at different location.So how should you solve this problem?

First.let's mark the target on a graph.



The black stick is the target,and the graphing calculator window sitting is above the graph.


So now,you should get the function set up. Y=-4.9x²+ax+b is the common form for a parabola in physics. -4.9 is the gravity,and x is the time frame(in put),a is the energy,and b is the height(y intercept of a parabola)


If the question asks you to find how much power does this bowman have to use in order to hit the target at the height of 60 meters.how would you solve it?


First,we set up an equation according to the information.Let's try to let the bowman to use 10 measures of his power Which will creat an equation as Y=-4.9x²+10x+60



which will creat a parabola graph as the following:


We can see that tge arrow flied for a little bit and begin to drop according to the gravity,and it didn't hit the target which located at (8,0).So let's try another equation.  how about Y=-4.9x²+40x+60?


We will see:


This one flied a little bit far from the target.SO doesn't work.Try the last one y=-4.9x²+31.6x+60.And we get:

The arrow hit's the target at 60 meters high and with 31.6 measures of his power!



This is just a small part of functions.Functions can do a lot more than we think.

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