An object is launched directly in the air at a speed of 144 feet per second from a platform located 12 feet in the air. the motion of the object can be modeled using the function f(t)=−16t2+144t+12, where t is the time in seconds and f(t) is the height of the object. when, in seconds, will the object reach its maximum height? do not include units in your answer.

After 2 seconds the object reach its maximum height of 80 feet.

Step-by-step explanation:

Consider the provided function.

The function is a downward parabola.

The object will reach its max height at the vertex of the parabola.

The vertex of the parabola is given by ,

Where the standard form is .

By comparing the provided function with the standard form.

a=-16, b=64 and c=16

Thus, the vertex are:

Now substitute the value of t in the provided function.

Hence, after 2 seconds the object reach its maximum height of 80 feet.

Explanation:

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