30 Points! A soccer ball hit from the ground into the air and is modeled by the function h(t)=-16t^2+48t+2 (see attachment)

A)

At t = 3/2

B)

36 feet

Step-by-step explanation:

The soccer ball is modeled by the function:

Where h(t) represents the height in feet of the ball over time t.

Note that this is a quadratic equation.

Part A)

Since this is a quadratic, the maximum height will be reached when the ball reaches its vertex.

So, we will find the x-coordinate of the vertex.

The vertex is given by:

In this case, a = -16 and b = 48. Thus, the t-coordinate is:

The ball will reach is maximum height at t = 3/2.

Part B)

To find the maximum height, we can simply substitute the value back into the function and evaluated. Therefore:

The maximum height of the ball is 36 feet.

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