What is the length of the line segment JK?

It should be 10. This is because the triangles are similar. On the bigger triangle, because one side is 12 and the top is 20, then if we take the smaller triangle we can set up a ratio. That same side is 6, which is half of 12. Half of 20 is 10, which represents the side youre looking for.

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