Michael reads 12 pages of a book in 18 minutes, 8 pages in 12 minutes, and 20 pages in 30 minutes. Is this a proportional relationship? If so, what is the constant of proportionality? What does it represent? Write an equation to represent this situation.

y = 1.5x

What you would do is divide all of the minutes by the amount of pages to find how long for each rate for one page. (ex. 18/12, michael reads 1 page in 1.5 minutes. 12/8, michael reads 1 page in 1.5 minutes. 30/20, michael reads one page in 1.5 minutes) Therefore, yes it is proportional, and the equation is y=1.5x (there is no y intercept)

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