Age 16 to 18 Challenge Level:
Find a quadratic graph which is at most 1 unit of distance away
from each of the six points
(x, y) = (\pm 1, 0), (\pm 2, 4), (\pm 3, 16)
Can you find the smallest distance from each of these points to
your quadratic, either exactly or to two decimal places?
Can you find another quadratic graph for which the largest of these
smallest distances from the points to the curve is smaller?
As an open extension, explore what you can say about configurations
of points at least one of which must necessarily lie more than one
unit of distance away from a quadratic.