2次函数,一般式化成顶点式～Y＝[100+x][100-1/2x] 先变成一般式,然后在化成顶点式．．写出详细过程

把它展开就是一般式：y=-1/2x平方＋50x+10000，再把有x的项化简得顶点式：y=-1/2(x-50)平方＋11250…谢啦！

Y=100*100+100*0.5X+X*100-0.5X^2
=-0.5X^2+50X+10000
=-0.5(X^2-100X)+10000
=-0.5((X^2-100X+50*50)-50*50)+10000
=-0.5(X-500)^2+1250+10000
=-0.5(X-500)^2+11250

y=10000-500x+100x-1/2x^2
=-1/2x^2-400x+10000
-b/2a=-400 4ac-b^2/4a=90000
所以：y=-1/2(x+400)^2+90000

Y=10000+100X-50X-1/2X^2=-1/2X^2+50X+10000(一般式）=-1/2（X^2-100X)+10000=-1/2(X-50)^2+11250(顶点式）

y=10000-500x+100x-1/2x^2
=-1/2x^2-400x+10000
=-(1/2x^2+400x)+10000
=-1/2(x^2+800x+400^2-400^2)+10000
=-1/2(x+400)^2+160000+10000
==-1/2(x+400)^2+170000

一般式 Y=-1/2X^2+50X+10000
顶点式 Y=-1/2(X-50)^2+11250
方法：一般式 先去括号，在合并同内向
顶点式 去括号，合并同内向得Y=-1/2X^2+50X+10000，提取公因式=-1/2 得-1/2（X^2-100X+2500-2500)+10000,计算得Y=-1/2(X-50)^2+11250