Algebra

This week we’ve talked about polynomials and their properties. Polynomials show up in the real world a lot more than you would think! Applications can be found in physics, economics, meteorology, and more.

One real-world example of a degree-two polynomial is the projectile motion equation used in physics:h left parenthesis t right parenthesis equals minus 1 half a t squared plus v subscript 0 t plus h subscript 0

Details about this formula can be found at the brainfuse.com website.

For example, if you hit a baseball at shoulder height (say about 4 f t comma space 6 space i n c h e s space minus space h subscript 0 equals 4.5 f t), you may have an initial velocity of aroundv subscript 0 equals 89.5 m p h. The force of gravity is about a equals 32 f t divided by s squared..

We can convert our miles to hour to feet per second (89.5 mph = 131.3 ft/s) and create an equation that would model the height of the ball at time t:

h left parenthesis t right parenthesis equals minus 1 half left parenthesis 32 right parenthesis t squared plus 131.3 t plus 4.5

Pick a baseball team average speed off the bat from this list. Pretend you are on that team and hitting a pitch. Using your height and the information in the table, create your own personalized equation as was done in the example above.

Once you have your equation, find the zeros and the vertex using the techniques covered this week in Chapter 3. Show all your work!

Compare the maximum height of your classmate’s baseball to your own. Do you think the difference is more from the difference in initial height of the bat or in the speed of the pitch?

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