y = x 2 − 2 m x + 3 m + 4 {\displaystyle {\begin{aligned}&y=x^{2}-2mx+3m+4\\\end{aligned}}}
x = − b 2 a = 2 m 2 = m ↓ | m | < 3 ↓ − 3 < m < 3 {\displaystyle {\begin{aligned}&x={\frac {-b}{2a}}={\frac {2m}{2}}=m\\&\downarrow \\&|m|<3\\&\downarrow \\&-3<m<3\\\end{aligned}}}
y = 4 a c − b 2 4 a 4 ∗ ( 3 m + 4 ) + 4 m 2 4 12 m + 16 − 4 m 2 4 − m 2 + 3 m + 4 ↓ − 6 < − m 2 + 3 m + 4 < 6 {\displaystyle {\begin{aligned}&y={\frac {4ac-b^{2}}{4a}}\\&{\frac {4*(3m+4)+4m^{2}}{4}}\\&{\frac {12m+16-4m^{2}}{4}}\\&-m^{2}+3m+4\\&\downarrow \\&-6<-m^{2}+3m+4<6\\\end{aligned}}}
− 6 < − m 2 + 3 m + 4 m 2 − 3 m − 10 < 0 ( m + 2 ) ( m − 5 ) < 0 ( m + 2 ) ( m − 5 ) = 0 m + 1 = − 2 : m 2 = 5 ↓ − 2 < m < 5 {\displaystyle {\begin{aligned}&-6<-m^{2}+3m+4\\&m^{2}-3m-10<0\\&(m+2)(m-5)<0\\&(m+2)(m-5)=0\\&m_{+}1=-2:m_{2}=5\\&\downarrow \\&-2<m<5\\\end{aligned}}}
− m 2 + 3 m + 4 < 6 − m 2 + 3 m − 2 < 0 ( m − 1 ) ( m − 2 ) < 0 ( m − 1 ) ( m − 2 ) < 0 m 1 = 1 ; m 2 = 2 ↓ m < 1 ; m > 2 {\displaystyle {\begin{aligned}&-m^{2}+3m+4<6\\&-m^{2}+3m-2<0\\&(m-1)(m-2)<0\\&(m-1)(m-2)<0\\&m_{1}=1;m_{2}=2\\&\downarrow \\&m<1;m>2\end{aligned}}}
− 3 < m < 3 {\displaystyle \ -3<m<3}
− 2 < m < 1 2 < m < 5 {\displaystyle {\begin{aligned}&-2<m<1\\&2<m<5\\\end{aligned}}}
1 < m < − 2 ; 2 < m < 3 {\displaystyle {\begin{aligned}1<m<-2;2<m<3\end{aligned}}}
