Which of the following scatterplots shows a ralationship that is appropriately modeled with the equation `y=- ax ^(2) + bx-c,` where a and c are negative and b is positive ?

Options

A.
B.
C.
D.

Answer

D

Explanation

Sketch in the lines of best fit for the answer choices. (A) and (D) are parabilas that open up, (B) is a parabola that opens doen, can (C ) is an exponetial curve. The equation that needs to be modeled is `y =- ax ^(2)+bx-c,` which is quadratic and graphs as a parabola. Eliminate (C ). Pay careful attention to the details "a and c are negative and b is positive. " The coefficient in front of the `x ^(2)` term determines whether the parabola opens up or down. The negative sign in front of the a multiplies by the negative value for a to create a positive coefficient in front of the `x ^(2)` term, which means that the parabola opens up. Eliminate (B). Finally, the c coefficient in the equatino determines the y-intercept for the graph. Again, the negative sign in front of c multiplies by the negative value of c to create a positive y-intercept. Eliminate (A) because the best fit parabola has a negative y-intercept (D) is correct.