\[\boxed{\mathbf{710\ (710).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]
\[(0;0);\ \ A\ \left( - 1;\ - \frac{1}{4} \right).\]
\[y = ax^{2} + bx + c\]
\[(0;0),\ то\ x = - \frac{b}{2a} = 0,\]
\[\ \ b = 0,\ \ y = a \cdot 0 + 0 + c,\]
\[\ \ c = 0\]
\[тогда\ \ y = ax^{2}\]
\[a \cdot ( - 1)^{2} = - \frac{1}{4},\ \ a = - \frac{1}{4}\]
\[тогда\ \ \ y = - \frac{1}{4}x^{2}\]
\[Ответ:y = - \frac{1}{4}x^{2}.\]