Four students compared their running speeds. Each student represented their data in a different format Select the names of all of the students who ran at a faster rate than Amy, based on the information given, where x is the time, in
minutes, and y is the distance traveled, in miles.
Amy ran 2 miles in 36 minutes.
y
Brian
10
Number of Mles
Chris
10
30 40X
Number of Minutes
Ethan
Number
Number
of Mles of Minutes
1.5 16.5
3
33
4.5 49.5
y = 42"

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

yes

step-by-step explanation:

they have to be opposite and reciprocal of eachother.

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