PLEASE HELP ME I'LL MAKE YOU BRAINLIEST In 1972, federal vehicle emission standards 3.4 grams hydrocarbons released per mile driven. By 2007, the standards allowed only 0.8 grams hydrocarbons per mile driven. What was the rate of change from 1972 to 2007? Please show work thank you

Work Shown:

x = year

y = amount of hydrocarbon emissions in grams, per mile driven

m = rate of change = slope

m = (y2 - y1)/(x2 - x1)

m = (0.8 - 3.4)/(2007 - 1972)

m = -2.6/35

m = -0.0742857 approximately

The approximate rate of change is about -0.0742857 grams per year. The negative rate of change indicates the per mile hydrocarbon amount has gone down by about 0.0742857 grams each year.

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