[tex]y=-x ^2 - 6x -5 \\ \\ standard \ form \\ \\y=ax+bx+c \\ \\V(p,q)\\ \\ p=\frac{-b}{2a}=\frac{-(-6)}{-2}=3\\ \\\Delta = b^{2}-4ac =14^{2}-4*1*(-51)=196+204=400 \\ \\q=\frac{-\Delta }{4a} =\frac{-400}{4}=100\\ \\V( 3,100)\\ \\x_{1}=\frac{-b-\sqrt{\Delta }}{2a} =\frac{-14- \sqrt{400}}{2}=\frac{-14-20}{2}= \frac{-34}{2}=-17\\ \\x_{2}=\frac{-b+\sqrt{\Delta }}{2a} =\frac{-14+ \sqrt{400}}{2}=\frac{-14+20}{2}= \frac{6}{2}=3 [/tex]
