(1) Ax

with non-zero A reduces by dividing through A: B'=B/A, C'=C/A to:

(2) x

This setting:

(3) -2p = B' = B/A <=> p = -B/(2A) and q = C'=C/A,

reduces to (4) x

The function y = x

(5) y = x

since:

(6) y= x

The translation { y'= y - (q-p

The point is that we are cutting all the time the

By the way notice that points (p,q) for which the corresponding equation touches the x-axis are precisely the points on the standard parabola y=x

Leaving the Ax

The dynamic figure changes by moving point (p,q). Points {s

For general properties of parabolas see Parabola.html . Relating to the standard equation of the parabola see ParabolaParameter.html .

ParabolaParameter.html

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