Parabola Property

Permute the coefficients a, b and c in the parabola y = a.x² + b.x + c and plot all six graphs to see some magic

Source: 
<p><span style="font-size:small">Created with <a href="http://www.risps.co.uk//" target="_blank" >RISP Website</a></span></p>

Result

a = 12 (slider from -20 to 20, step 0.01)
b = -14.5 (slider from -20 to 20, step 0.01)
c = 2.5 (slider from -20 to 20, step 0.01)
Condition: a^(2) + b^(2) + c - 2 * (a + b + c)
SubCondition1: a^(2) + b^(2) - 4 * c
SubCondition2: b^(2) + c^(2) - 4 * a
SubCondition3: c^(2) + a^(2) - 4 * b
d: y = a * x^(2) + b * x + c
e: y = a * x^(2) + c * x + b
f: y = b * x^(2) + a * x + c
g: y = b * x^(2) + c * x + a
h: y = c * x^(2) + a * x + b
k: y = c * x^(2) + b * x + a
j = false