Question 443093
(0,1) tells us that c = 1  since 1 = 0 + 0 +c

Then 1 = 4a + 2b + 1 
     -1 =16a + 4b + 1
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0 = 4a + 2b
-2 = 16a + 4b

*[invoke linear_substitution "a", "b", 4, 2, 0, 16, 4, -2 ]

So a = -(1/4) b = 1/2  c =1

So the quadratic is {{{-(1/4)x^2 + (1/2)x + 1}}}