If your equation is [tex]y=- \frac{1}{4} x^{2} + \frac{1}{2} x- \frac{13}{4} [/tex], then the domain is all real numbers (-∞, ∞).
If your equation is [tex]y = - \frac{1}{4 x^{2} } + \frac{1}{2x} - \frac{13}{4} [/tex],
then the domain is all real numbers except zero (-∞, 0)∪(0, ∞)