Amedical plan requires a patient to pay a $25.00 copay plus 20% of all charges incurred for a medical procedure. if the average bill for a patient is between $200 and $800, find the range of the original bill.

It is stated that the total bill the patient would only pay would be the $25 plus 20% of the original bill. Therefore this would mean that:

25 + 0.2 * X = 200         ---> 1

25 + 0.2 * X = 800         ---> 2

Where X represents the original bill.

Calculating for X in equation 1:

25 + 0.2 * X = 200

0.2 * X = 175

X = 875

Calculating for X in equation 2:

25 + 0.2 * X = 800

0.2 * X = 775

X = 3875

Therefore the original bill ranges from $875 to $3875. The equality equation would be:

$875 ≥ X ≥ $3875

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