Aball is thrown straight up into the air. the height, in feet, h(t), of the ball collected over t seconds is shown in the table.

which statement is true?

the initial height of the ball is 96 feet.
the ball will hit the ground between 2 and 3 seconds after it was thrown.
the maximum height of the ball must be 96 feet.
the maximum height of the ball was 2.5 seconds after it was thrown.

The maximum height of the ball was 2.5 seconds after it was thrown.

the answer is D

Option D is correct

The maximum height of the ball was 2.5 seconds after it was thrown.

Step-by-step explanation:

let a and b are the zeros of the function f(x) then;

f(x)= k(x-a)(x-b)

where, k is the coefficient.

As per the statement:

A ball is thrown straight up into the air. The height, in feet, h(t), of the ball collected over t seconds is shown in the table.

From the given table:

At t = 0

h(0)= 0

At t = 5

h(5) = 0

⇒0 and 5 are the zeros the function h(t)

then by definition we have;

⇒                    .....[1]

Now substitute any point from the table i.e, (2, 96) in [1] to find k;

Simplify:

Divide both sides by -6 we have;

or

k = -16

then, we have the equation for h(t) as:

⇒          ....[1]

Initial height of the ball:

h(0) = 0

To find the maximum height of the ball.

A quadratic equation .....[2], the the axis of symmetry is given by:

On comparing [1] and [2] we have;

a =-16 and b = 80 then;

sec

⇒the maximum height of the ball was 2.5 second.

Therefore, the statement which is true is: The maximum height of the ball was 2.5 seconds after it was thrown.

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