\[y = 2x^{2} + bx + c;\ \ \ A( - 1; - 10).\]
\[x = - \frac{b}{2a}:\]
\[- 1 = - \frac{b}{4}\]
\[- b = - 4\]
\[b = 4.\]
\[x = - 1:\]
\[- 10 = 2 \cdot 1 - 4 + c\]
\[c = - 10 + 2\]
\[c = - 8.\]
\[Ответ:b = 4;\ \ c = - 8.\]