Step-by-step explanation:
As we move from left to right, and as x accordingly varies from 1 to 6 , we see the y value first increasing, then reaching an actual or approximate maximum of 335 for x = 4, and then decreasing as x continues to increase.
This is the graph of a parabola opening down, which focuses our attention on answer choices A and D only.
Let's check out A: Use synthetic division to determine the approximate value of y when x = 3 (this is a somewhat arbitrary choice for x):
3 / -9.16 73.04 183.3
-27.48 -136.68
-9.16 -45.56 46.62 Thus, the value of the first function at
x = 3 is approx. 46.62, which is rather
far from the expected 316.
Let's check out D: y = -9.16x^2 - 73.04x + 183.3
Again let x = 3. The smaller the remainder in synthetic division, the closer this equation predicts the y value:
3 / -9.16 -73.04 183.3
-27.48 -301.56
-9.16 -100.52 -118.26 This remainder is even further
from the expected value (316)
The first equation is a (somewhat) better fit than is the fourth. The second and third equations are totally inappropriate because their graphs open UP instead of down.