Billy's plant grows at least 2 inches a month.

graph the solution to the scenario by dragging and dropping a circle/arrow onto the number line.

best answer gets brainliest

Step-by-step explanation:

Here we are given that the plant growth is fixed by 2 inches for every month.

hence ,

if we assume that the plant had zero height at beginning , when the time was also zero, then in the next month that is 1st month the height of the plant will be 2 inches, similarly in the 2nd month the height will be 4 inches , for the third month the height of the plant will be 6 inches and so on.

So, if we plot them on a graph , taking time in month on x axis and height of the plant on y axis , the pattern of growth as mentioned above will give us few coordinates like,

(0,0) , (1,2) , (2,4) , (3,6) and so on..

hence from here we can determine equation which refers the above situation by using two point form of an equation . The two point form is given as

where

and are and respectively

substituting them in the above formula we get

Hence we get out scenario , in equation as

Note:

this is the situation when the height of the plant was considered 0 at time 0 . however , if the initial height of the plant was k ( assumption )

The equation would have been like this

This is because in both the cases the slope of the line would be same , as slope represents the rate of increase of y with respect to x . in this case it would be the increased in the height of the plant with respect to the months Where k represent the value of y at x= 0 , or the height of the plant at time 0 month.

Please refer to the image attached with this.

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