Tọa độ dỉnh của (P) là: \(I \left(\right. - \frac{b}{2 a} ; \frac{- \Delta}{4 a} \left.\right) \Rightarrow I \left(\right. 1 ; - 4 m - 2 \left.\right)\)

Để I thuộc \(y = 3 x - 1\)

\(\Rightarrow - 4 m - 2 = 3.1 - 1\)

\(\Rightarrow m = - 1\)

6.a.

Với \(a \neq 0\)

 \(\left{\right. 64 a + 8 b + c = 0 \\ - \frac{b}{2 a} = 5 \\ \frac{4 a c - b^{2}}{4 a} = 12\)  \(\Leftrightarrow \left{\right. 64 a + 8 b + c = 0 \\ b = - 10 a \\ 4 a c - b^{2} = 48 a\)

\(\Leftrightarrow \left{\right. c = - 64 a - 8 b = - 64 a - 8 \left(\right. - 10 a \left.\right) = 16 a \\ b = - 10 a \\ 4 a c - b^{2} = 48 a\)

\(\Rightarrow 4 a . 16 a - \left(\left(\right. - 10 a \left.\right)\right)^{2} = 48 a\)

\(\Rightarrow a = - \frac{4}{3} \Rightarrow b = \frac{40}{3} \Rightarrow c = - \frac{64}{3}\)

Hay pt (P): \(y = - \frac{4}{3} x^{2} + \frac{40}{3} x - \frac{64}{3}\)