Steve and Mark are both filling their own bucket with water. -Steven begins with 8 cups of water in his bucket, and fills the bucket at a rate of 2 cups per second.
- The number of cups of water, W, in Mark's bucket after t seconds is represented by the equation w= 8t + 1
Which statement is true:
A. Mark begins with more cups of water in his bucket
B. Mark begins with the same amount of water as Steven
C. Mark fills his bucket at a faster rate than Steven
D. Mark fills his bucket at the same rate as Steven

D

Step-by-step explanation:

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step-by-step explanation:

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