You drop a ball from a stair case that is 36 ft high. By the time you get down the stairs to measure the height of the bounce, the ball has bounced four times and has a height of 2.25 ft after its fourth bounce. How high did the ball bounce after it first hit the floor?

The height should be 18 feet.

Given that,

Based on the above information, the calculation is as follows:

The first height is 36 feet.

Now after the first bounce, it will be 36r

Here r is the ratio of the height

In the second bounce, the height is

In the third bounce, the height is

In the fourth bounce, the height is , and this value is 2.25 ft, so:

Now

r = 0.5

Now  

So, after the first bounce, the height is:

= 36r

= 36(0.5)

= 18 feet

Therefore we can conclude that The height should be 18 feet.

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18 feet

Step-by-step explanation:

After each bounce, the ball reaches only a percentage of the maximum height it reached before.

The first height is 36 feet, after the first bounce, it will be 36*r, where r is the ratio of the height the ball can still reach by the previous maximum height.

In the second bounce, the height is 36*r^2

In the third bounce, the height is 36*r^3

In the fourth bounce, the height is 36*r^4, and this value is 2.25 ft, so:

36*r^4 = 2.25

r^4 = 2.25/36

r^4 =  0.0625

r = 0.5

So, after the first bounce, the height is:

36*r = 36*0.5 = 18 feet

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1