The table shows the soil density of several soil samples at different depths. Depth (m) 1 5 6 8 10 12 14 21 23 24 28
Soil density ( )
1045 1063 1102 1140 1191 1232 1249 1254 1265 1268 1273

(a) Write the quadratic regression equation that models the data. Let x = depth below the surface and let y = soil density.
(b) Use the equation to estimate the soil density of a sample at a depth of 20 m. Show your work.

21

step-by-step explanation:

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

i dont know what you want me to answer for this but im guessing 2: 11?