the data in the table represents a companys profit based on the number of items produced.\nprofit based on…

Explanation:

Step1: Substitute x = 100 into each equation

For $y=-1.026x^{2}+1016.402x - 162075$: $y=-1.026\times(100)^{2}+1016.402\times100 - 162075$ $y=-10260+101640.2 - 162075=-70494.8$ For $y=-1.036x^{2}+1024.771x - 163710$: $y=-1.036\times(100)^{2}+1024.771\times100 - 163710$ $y=-10360+102477.1 - 163710=-71592.9$ For $y = 298.214x-66317.667$: $y=298.214\times100 - 66317.667=29821.4 - 66317.667=-36496.267$ For $y = 196.2x-18710$: $y=196.2\times100 - 18710=19620 - 18710 = 910$

Step2: Substitute x = 200 into each equation

For $y=-1.026x^{2}+1016.402x - 162075$: $y=-1.026\times(200)^{2}+1016.402\times200 - 162075$ $y=- 41040+203280.4 - 162075=-175.6$ For $y=-1.036x^{2}+1024.771x - 163710$: $y=-1.036\times(200)^{2}+1024.771\times200 - 163710$ $y=-41440+204954.2 - 163710= - 3195.8$ For $y = 298.214x-66317.667$: $y=298.214\times200 - 66317.667=59642.8 - 66317.667=-6674.867$ For $y = 196.2x-18710$: $y=196.2\times200 - 18710=39240 - 18710 = 20530$

Step3: Substitute x = 300 into each equation

For $y=-1.026x^{2}+1016.402x - 162075$: $y=-1.026\times(300)^{2}+1016.402\times300 - 162075$ $y=-92340+304920.6 - 162075 = 50505.6$ For $y=-1.036x^{2}+1024.771x - 163710$: $y=-1.036\times(300)^{2}+1024.771\times300 - 163710$ $y=-93240+307431.3 - 163710 = 50481.3$ For $y = 298.214x-66317.667$: $y=298.214\times300 - 66317.667=89464.2 - 66317.667 = 23146.533$ For $y = 196.2x-18710$: $y=196.2\times300 - 18710=58860 - 18710 = 40150$

Step4: Compare the results with the table values

By comparing the calculated y - values with the values in the table for different x - values, the equation $y=-1.026x^{2}+1016.402x - 162075$ gives values that are closest to the actual profit values in the table.

Answer:

$y=-1.026x^{2}+1016.402x - 162075$