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:

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

For example, if you hit a baseball at shoulder height (say about , you may have an initial velocity of around. The force of gravity is about .

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:

For the discussion this week we will use this equation in a baseball application. Techniques from 1.4 and 3.1 will be used. Show all of your work!

1. Pick a baseball player’s average exit velocity from this list and convert it to feet per second.
2. Estimate the height in feet that the ball would be hit and plug this and your velocity into the position equation. Give the equation.
3. Find the maximum height of the ball (vertex).
4. Find when the ball hits the ground (zeros).
5. What role do you think the angel of the hit would play in modifying this equation or the values?

Compare the maximum height of your classmate’s baseball to your own. What factors do you think contribute most to the differences in your values? Explain.

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