二次函数公式法

\[\Large y=ax^2+bx+c \]

\[\Large y=a(x^2+\dfrac{b}{a}x+\dfrac{c}{a}) \]

\[\Large y=a(x^2+2\times x\times \dfrac b {2a}+\dfrac c a) \]

\[\Large y=a[x^2+2x\dfrac b {2a}+(\dfrac b {2a})^2-(\dfrac b {2a})^2+\dfrac c a] \]

\[\Large y=a[(x+\dfrac b {2a})^2-\dfrac{b^2}{4a^2}+\dfrac c a] \]

\[\Large y=a(x+\dfrac b {2a})^2-\dfrac{b^2}{4a}+c \]

\[\Large y=a(x+\dfrac b {2a})^2-\dfrac{b^2}{4a}+\dfrac {4ac}{4a} \]

\[\Large y=a(x+\dfrac b {2a})^2+\dfrac{4ac-b^2}{4a} \]

因此其顶点坐标为 \(\Large (-\dfrac b {2a},\dfrac{4ac-b^2}{4a})\)