Question

已知抛物线y=ax^2+bx+c的顶点是（-1,2）,且a+b+c+2=0.

Answer 1

y=(x+b/2a)^2+(4ac-b^2)/4a

x=-1,y=2代入

-b/2a=-1 b=2a

(4ac-b^2)/4a=(4ac-4a^2)/4a=c-a=2 c=a+2

b=2a c=a+2代入a+b+c+2=0

a+2a+a+2+2=0

4a=-4 a=-1

b=-2 c=1

抛物线解析式为y=-x^2-2x+1