1 2 , 1 3 , 1 4 , 4 5 , 5 6 {\displaystyle {\frac {1}{2}},{\frac {1}{3}},{\frac {1}{4}},{\frac {4}{5}},{\frac {5}{6}}}
5 6 3 5 4 {\displaystyle {\sqrt {5}}{\sqrt[{3}]{6}}{\sqrt[{4}]{5}}}
− b ± b 2 − 4 a c 2 a {\displaystyle {\frac {-b\pm {\sqrt {b^{2}-4ac}}}{2a}}}
y = f ( x ) = a x 2 + b x + c = a [ x 2 + b a x + c a ] = a [ x 2 + 2 ∗ b 2 a x + ( b 2 a ) 2 − ( b 2 a ) 2 + c a ] {\displaystyle y=f(x)=ax^{2}+bx+c=a[x^{2}+{\frac {b}{a}}x+{\frac {c}{a}}]=a[x^{2}+2*{\frac {b}{2a}}x+({\frac {b}{2a}})^{2}-({\frac {b}{2a}})^{2}+{\frac {c}{a}}]} = a [ ( x + b 2 a ) 2 − b 2 4 a 2 + 4 a c 4 a 2 ] = a [ ( x + b 2 a ) 2 − b 2 − 4 a c 4 a 2 ] {\displaystyle =a[(x+{\frac {b}{2a}})^{2}-{\frac {b^{2}}{4a^{2}}}+{\frac {4ac}{4a^{2}}}]=a[(x+{\frac {b}{2a}})^{2}-{\frac {b^{2}-4ac}{4a^{2}}}]} = a [ ( x + b 2 a ) 2 − ( b 2 − 4 a c 4 a 2 ) 2 ] = a [ ( x + b 2 a ) 2 − ( b 2 − 4 a c 2 a ) 2 ] {\displaystyle =a[(x+{\frac {b}{2a}})^{2}-({\sqrt {\frac {b^{2}-4ac}{4a^{2}}}})^{2}]=a[(x+{\frac {b}{2a}})^{2}-({\frac {\sqrt {b^{2}-4ac}}{2a}})^{2}]} = a [ ( x + b 2 a + b 2 − 4 a c 2 a ) ( x + b 2 a − b 2 − 4 a c 2 a ) ] = a [ x + b ± b 2 − 4 a c 2 a ] {\displaystyle =a[(x+{\frac {b}{2a}}+{\frac {\sqrt {b^{2}-4ac}}{2a}})(x+{\frac {b}{2a}}-{\frac {\sqrt {b^{2}-4ac}}{2a}})]=a[x+{\frac {b\pm {\sqrt {b^{2}-4ac}}}{2a}}]} = a [ x − − b ± b 2 − 4 a c 2 a ] {\displaystyle =a[x-{\frac {-b\pm {\sqrt {b^{2}-4ac}}}{2a}}]} − b ± b 2 − 4 a c 2 a {\displaystyle {\frac {-b\pm {\sqrt {b^{2}-4ac}}}{2a}}}
A ( x 1 , y 1 ) , B ( x 2 , y 2 ) {\displaystyle A(x_{1},y_{1}),B(x_{2},y_{2})} 距离 = ( x 1 − x 2 ) 2 + ( y 1 − y 2 ) 2 {\displaystyle ={\sqrt {(x_{1}-x_{2})^{2}+(y_{1}-y_{2})^{2}}}} 中点座标 = ( x 1 + x 2 2 , y 1 + y 2 2 ) {\displaystyle =({\frac {x_{1}+x_{2}}{2}},{\frac {y_{1}+y_{2}}{2}})} A B → = ( x 2 − x 1 , y 2 − y 1 ) {\displaystyle {\overrightarrow {AB}}=(x_{2}-x_{1},y_{2}-y_{1})}
![{\displaystyle {\sqrt {5}}{\sqrt[{3}]{6}}{\sqrt[{4}]{5}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f87efc4ecd7d34423356f036d2a584279b7b779f)
![{\displaystyle y=f(x)=ax^{2}+bx+c=a[x^{2}+{\frac {b}{a}}x+{\frac {c}{a}}]=a[x^{2}+2*{\frac {b}{2a}}x+({\frac {b}{2a}})^{2}-({\frac {b}{2a}})^{2}+{\frac {c}{a}}]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b4abdabbc6188d81193bb396b985fc0a46bbe400)
![{\displaystyle =a[(x+{\frac {b}{2a}})^{2}-{\frac {b^{2}}{4a^{2}}}+{\frac {4ac}{4a^{2}}}]=a[(x+{\frac {b}{2a}})^{2}-{\frac {b^{2}-4ac}{4a^{2}}}]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0bdffd6a22fad26ebbc57fcf4e944f611c0730fa)
![{\displaystyle =a[(x+{\frac {b}{2a}})^{2}-({\sqrt {\frac {b^{2}-4ac}{4a^{2}}}})^{2}]=a[(x+{\frac {b}{2a}})^{2}-({\frac {\sqrt {b^{2}-4ac}}{2a}})^{2}]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8f255fa6f83ea1b8915f4f676607a4808861ab95)
![{\displaystyle =a[(x+{\frac {b}{2a}}+{\frac {\sqrt {b^{2}-4ac}}{2a}})(x+{\frac {b}{2a}}-{\frac {\sqrt {b^{2}-4ac}}{2a}})]=a[x+{\frac {b\pm {\sqrt {b^{2}-4ac}}}{2a}}]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/29f5aa58e419d185764fd258430e815f039482fa)
![{\displaystyle =a[x-{\frac {-b\pm {\sqrt {b^{2}-4ac}}}{2a}}]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/50ede7d1fa49902c93ca91add02de6c5e53e862d)
