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With all the answers I received before, I was able to build this code, with a small improvement.

def signe(valeur):
    if valeur < 0:
        return(fr"-{latex(-valeur)}")
    else:
        return(fr"+{latex(valeur)}")

def cform(a, alpha, beta):  # cform means canonical form a (x - alpha)^2 + beta
    if a == 1:
        fc_str = fr"\displaystyle \left(~{latex(x-alpha)}~\right)^2 {signe(beta)}"
    elif a == -1:
        fc_str = fr"\displaystyle -\left(~{latex(x-alpha)}~\right)^2 {signe(beta)}"
    else:
        fc_str = fr"\displaystyle {latex(a)}\left(~{latex(x-alpha)}~\right)^2 {signe(beta)}"
    return fc_str

def fform(a, x1, x2): # fform means factored form a (x - x1) (x - x2)
    if a==1:
        ff_str = fr"\displaystyle \left(~{latex(x-x1)}~\right)\left(~{latex(x-x2)}~\right)"
    elif a==-1:
        ff_str = fr"\displaystyle -\left(~{latex(x-x1)}~\right)\left(~{latex(x-x2)}~\right)"
    else:
        ff_str = fr"\displaystyle {latex(a)}\left(~{latex(x-x1)}~\right)\left(~{latex(x-x2)}~\right)"
    return ff_str

The improvment is to write \left(~{latex(x-alpha)}~\right)^2 instead of \left(~{latex((x-alpha)^2)}~\right) which involves a calculation. Placing x-alpha in latex{ } prevents this calculation and we remove the sign problem for alpha (I noticed this when I built the fform function and I applied it for function cform).

For the sign of beta, I imagined the function signe that it is possible to use in other places.

I'm sure this can be improved.

Thanks for all the answers that were very helpfull, I've learnd a lot.