The function f(x) = -5x² + 20x + 55 models the height of a ball x seconds after it is thrown into the air. What is the total time that the ball is in the air?

The ball is in the air for about 5.873 seconds.

Step-by-step explanation:

The function:

Models the height of a ball x seconds after it is thrown in the air.

And we want to find the total time the ball is in the air.

So, we can simply find the time x at which the ball lands. If it lands, its height f above the ground will be 0. Thus:

We will solve for x. Dividing both sides by -5 yields:

The equation is unfactorable, so we can use the quadratic formula:

In this case, a = 1, b = -4, and c = -11. So:

Evaluate:

Approximate:

Since time cannot be negative, our only solution is the first choice.

So, the ball is in the air for about 5.873 seconds.

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step-by-step explanation:

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