Question

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

A 2-column table with 6 rows titled Height of Ball over Time. The first column is labeled t with entries 0, 1, 2, 3, 4, 5. The second column is labeled h(t) with entries 0, 64, 96, 96, 64, 0.
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 reached 2.5 seconds after it was thrown.

Answer 1

Option D is the right option. The maximum height of the ball was 2.5 seconds after it was thrown.

Let b and h be the zeros of the function f(x). If this statement is true, then f(x)= k(x-a)(x-b) would be our equation. Let k be our coefficient.

From the given table,

At t = 0

h(0)= 0

At t = 5

h(5) = 0

So, 0 and 5 are the zeros of the function h(t).

h(t)=k(t-0)(t-5)

h(t)=k(t)(t-5)

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

96=k(2)(2-5)

96=k(2)(-3)

Now, we simplify!

96=-6k

k=-16

Now, we have the equation for h(t)

h(t)=-16(t-5)

h(1)=-16t^2+80t

Initial height of the ball: h(0) = 0 To find the maximum height of the ball, we will use the quadratic equation y=ax^2+bx+c.....[2], the the axis of symmetry is given by: x=-b/2a

Now that we know b= -16 and h= 80 we can perform this equation to find out for t:

t=-80/2(-16)=80/32=2.5 seconds

We can now come to the conclusion that the statement "The maximum height of the ball was reached 2.5 seconds after it was thrown." is the one true statement.

I hope this helps!! o(〃＾▽＾〃)o