Calculate Fourier Transform

Question

I have question for which i am stuck at

Calculate the Fourier Transform of $f(x) = e^-((x-1)^2)/4$

I am not sure if my answer is correct since it makes no sense...

Answer 1

$$ f(x) = e^{\left(-\frac{1}{4} \, {\left(x - 1\right)}^{2}\right)} $$ applying the definition of the fourier transform yields $$ \mathfrak{F} (\xi) = \int_{-\infty}^{\infty} e^{-2 \, \pi x \xi - \frac{1}{4} \, {\left(x - 1\right)}^{2}} dx $$ $$ = 2 \, \sqrt{\pi} e^{\left(4 \, \pi^{2} \xi^{2} - 2 \, \pi \xi\right)} $$