The equation ​ yˆ=−6.2x2+51.5x+10.2 ​ approximates the average number of cars that pass through an intersection x hours after 3:00 p.m. What is the best estimate for the average number of cars that pass through the intersection at 6:30 p.m.?

Notice that form 3 pm to 6:30 pm 3.5 hours have passed.
Since the function [tex]y=-6 x^{2} +51.5x+10.2[/tex] represent the average number of cars that pass through an intersection x hours after 3:00 p.m, we are going to replace [tex]x[/tex] with 3.5 to find the average number of cars that pass through the intersection at 6:30 p.m
[tex]y=-6 x^{2} +51.5x+10.2[/tex]
[tex]y=-6 (3.5)^{2} +51.5(3.5)+10.2[/tex]
[tex]y=-6(12.25)+180.25+10.2[/tex]
[tex]y=-73.5+190.45[/tex]
[tex]y=116.95[/tex]

We can conclude that the average number of cars that pass through an intersection at 6:30 pm is approximately 117.