A teenager who is 5 feet tall throws an object into the air. The quadratic function LaTeX: f\left(x\right)=-16x^2+64x+5f ( x ) = − 16 x 2 + 64 x + 5 is where f(x) is the height of the object in feet and x is the time in seconds. When will the ball be 10 feet in the air?

At approximately x = 0.08 and x = 3.92.

Step-by-step explanation:

The height of the ball is modeled by the function:

Where f(x) is the height after x seconds.

We want to determine the time(s) when the ball is 10 feet in the air.

Therefore, we will set the function equal to 10 and solve for x:

Subtracting 10 from both sides:

For simplicity, divide both sides by -1:

We will use the quadratic formula. In this case a = 16, b = -64, and c = 5. Therefore:

Substitute:

Evaluate:

Simplify the square root:

Therefore:

Simplify:

Approximate:

Therefore, the ball will reach a height of 10 feet at approximately x = 0.08 and x = 3.92.

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