Now, let's look at a few more examples using our same equation, h(t) = -16t² + 57.3t + 4.

What does it mean to take this equation and set it equal to a certain number (like 20.0) and then solve the equation? In other words, if you solve the equation: 20.0 = -16t² + 57.3t + 4, what will your solution in terms of t actually mean?

If it is helpful to you, here is a graph of the functions h(t) = -16t² + 57.3t + 4 and h(t) = 20.0.

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Check Your Answer

The positive solution would tell you how many seconds elapse before the ball is exactly 20.0 feet in the air.

Go ahead and solve this equation: 20.0 = -16t² + 57.3t + 4. Again, if you don’t have your graphing calculator handy, click here to access a website that will generate roots for a quadratic function.

If you are using the website, you will need to set your equation equal to zero by subtracting 20 from each side. You may then use the website to solve the following equation: 0 = -16t² + 57.3t - 16. What are your two solutions?

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Check Your Answer

t ≈ 0.31, 3.28

Interpret the meaning of the solution t ≈ 0.31

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The ball reaches 20 ft above the ground on the way up at t ≈ 0.31. Note: the function is increasing towards the vertex therefore the ball is on the way up.

Now interpret the meaning of the solution t ≈ 3.28

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Check Your Answer

The ball reaches 20 ft off the ground on the way down at t ≈ 3.28. Note: the function is decreasing away from the vertex therefore it is on the way down.