Given that a,b, and c are constants and that `a gt 0,` which of the following is the equation for the line of best fit for the above scatterplot ?

Options

A. `y = ax +b`
B. `y = a ^(bx)`
C. `y =-ax ^(2) +bx+c`
D. `y = ax ^(2)+bx+c`

Answer

D

Explanation

The line of best fit for this scatterplot is curved, so it is not a straight line as would be created by the linear equation `y =ax +b.` Eliminate (A).
The exponential equation `y =a ^(bx)` would results in a curve that opens upward in one direction. The lines of best fit of the scatterplot opens upward in two directions, so (B) is incorrect.
Quadratic equations create parabolas when graphed, but the negative coefficient of the `x ^(2)` term means that (C ) would be a doenward-opening parabola rather than the upward-opening of the scatterplot. Thus, (D) is correct since that since that equation would be graphed as an upward-opening parabola.