The ledger, turned sideways

Nothing new is proved on this page. Every feature you are about to see is something you already established without it.

cutproduct

The table comes first. Fill it before you draw anything.

product against cut   assessor's rule (62,500)   overcharge

Overlays

Turn on an overlay. Each one is a fact you proved algebraically; the page will say which.

Demand a product

Drag the line. Count where it meets the curve. This is the only question the picture answers faster than the algebra does.

The discipline of this page. For every feature you can see, you should be able to name where you proved it: the ends at 0 and 500 from the factored form, the single peak from 62500-(x-250)^2 and the fact that a square is never negative, the mirror from the \pm d pairing, the number of crossings from whether d^2 comes out positive, zero or negative. If you can do that, the picture is a transcription and you have lost nothing by having waited for it. If you cannot, go back — the picture is doing work it is not entitled to do.