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 To Explore Quadratics 
       on  the Pythabacus

STEP1:Left Click Check Button.
STEP2:Counting From the Rightmost Gold Bead, Left Click a Gold Bead at a position equal any Number. Click Right Arrow (CRA). In the equation 
X"- BX + C = Y, this step generates (B), which equals the displaced gold beads. 
STEP3:Left click another  gold  beads in or out of the displaced group (B). CRA. Of the equation 
(x +/- a)*(x +/- b) = y, this step generates (a), the bead clicked in step 3 plus the total number of gold beads to its right, while (b) equals (B) - (a). If (B)>(a), the quadrilateral of brown beads above and to the left of of the a-group equals the product of (a) times (b), equals (C) in the equation 
X" - BX + C = Y and C is positive. If (B)<(a) the quadrilateral of brown beads above and to the right of the displaced group plus the square of the number of gold beads in the displaced group equals (C) and (C) is negative. 
STEP4:Left click another  gold bead in any group. CRA. In the equation 
(x +/- e)*(x +/- f)=0, this step generates (e), the bead clicked in step 4 plus the total number of gold beads to its right, while (f) equals (B)-(e).  
STEP5:Left rightmost gold bead and click left arrow to review steps below.
 
 
Hover mouse over gold beads until bead flashes and beeps.
Step A: 
To solve a given factorable equation, such as the equation above generated by our manipulations of the Pythabacus, first push to the right a group of beads equal the factor of the equation's second term. In other words, Left click the bead your mouse now hovers over and CRA six times. 
 Hover mouse over gold beads until bead flashes and beeps.
Step B: 
Second, if the third term of the equation is positive, then partition the first group of beads to  reveal  a quadrilateral of brown beads equal the third term, the product of the parted beads. If the third term of the equation is negative, then to the left of the first group bead push to the right a group of beads that includes a triangle with a number of base beads that when multiplied by the total number of bead not still resting on the left post equals the third term. In other words, Left click the bead your mouse now hovers over and CRA 
 Hover mouse over gold beads until bead flashes and beeps.
Step C:
Repeat step B, but for the third term substitute the third term minus the value of (Y) or  (C1-Y). In other words, Left click the bead your mouse now hovers over and CRA. (X1) and (X2), the roots to the equation will equal, for (X1),  the total number of gold beads to the right of the last bead pushed, and for (X2), the first group of beads minus the last group of beads.