Question

The data in the table represents a company’s profit based on the number of items produced.

A 2-column table with 6 rows. The first column is labeled items produced (x) with entries 100, 200, 300, 400, 500, 600. The second column is labeled dollars of profit (y) with entries negative 70,500; 50; 50,100; 80,300; 90,400; 78,000.
Which equation best represents the data?

y = –1.026x2 + 1016.402x – 162075
y = –1.036x2 + 1024.771x – 163710
y = 298.214x – 66317.667
y = 196.2x – 18710

Answer 1

y = –1.026x^2 + 1016.402x – 162075

Reason: this concave-down quadratic matches the data very closely. For x = 100,200,300,400,500,600 it predicts approximately -70,695; 165; 50,506; 80,326; 89,626; 78,406, which are all very near the given values (–70,500; 50; 50,100; 80,300; 90,400; 78,000). The other quadratic and the linear models give larger discrepancies.