But what if you wanted to determine a?
y==a(x-b)(x-c)
Depending on one's equation, "sometimes" this may work:
equ = -24-6 x+3 x^2
FullSimplify[equ,ComplexityFunction->LeafCount]
3 (-4+x) (2+x)
Just to add: Both return the same equation to plot...
MinimalPolynomial[3/2+I Sqrt[7]/2,x]
4-3 x+x^2
MinimalPolynomial[3/2-I Sqrt[7]/2,x]
4-3 x+x^2
