Example

Using 16t2+250-16t^2 + 250 to Model the Height of a Dropped Ball

To apply the process of evaluating a polynomial function to a real-world scenario, consider a ball dropped from a 250250-foot building. The height of the ball in feet after tt seconds is given by the function h(t)=16t2+250h(t) = -16t^2 + 250. To determine the ball's height at t=2t = 2 seconds, substitute 22 into the function: h(2)=16(2)2+250h(2) = -16(2)^2 + 250. Simplify the exponent to obtain 16(4)+250-16(4) + 250. Multiplying 16-16 by 44 gives 64-64, and adding 250250 results in 186186. Therefore, the height of the ball after 22 seconds is 186186 feet.

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Updated 2026-04-29

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