\(\left(a\right):E\left(-1;5\right)\in\left(P\right)\Leftrightarrow a-b+2=5\Leftrightarrow a-b=3\Rightarrow\) Sai
\(\left(b\right):\) \(\left(P\right)\) có trục đối xứng \(x=1\) có nghĩa là \(x=\dfrac{-b}{2a}=-1\Leftrightarrow2a-b=0\Rightarrow\) Đúng
\(\left(c\right):\) \(M;N\in\left(P\right)\Leftrightarrow\left\{{}\begin{matrix}a+b+2=0\\a-b+2=0\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}a=-2\\b=0\end{matrix}\right.\)
\(\Rightarrow a+2024b=-2+2024.0=-2\Rightarrow\) Đúng
\(\left(d\right):\) \(S\) có hoành độ \(x=-\dfrac{b}{2a}=-1\Leftrightarrow2a-b=0\left(1\right)\)
Tung độ \(S\) là \(a-b+2=-\dfrac{3}{2}\Leftrightarrow a-b=-\dfrac{7}{2}\left(2\right)\)
\(\left(1\right);\left(2\right)\Rightarrow\left\{{}\begin{matrix}a=\dfrac{7}{2}\\b=7\end{matrix}\right.\)
\(\Rightarrow2a+b=2.\dfrac{7}{2}+7=14⋮14\Rightarrow\) Đúng
