The ratio of ed’s cars to pete’s cars was 5: 2 at first. after ed gave 30 cars to pete, they had an equal amount of cars each. how many cars did they have altogether?

The number of "ratio units" differs by 3. If 1.5 is subtracted from the high number and the same value added to the low number, the ratio would be 3.5:3.5, or 1:1. We conclude that 1.5 "ratio units" corresponds to 30 cars, so each "ratio unit" represents 20 cars.

The two have a total of 5+2 = 7 "ratio units" so have a total of 140 cars.

Do you need with the x value for the minimum? its always between the two intercepts for a parabola