Question

若抛物线的顶点在x轴上,对称轴是直线x=-1,与y轴交于点A(0,-3),求此抛物线的解析式

Answer 1

y=ax^2+bx+c =a(x+b/2a)^2+(b^2/4a-c)

x1+x2=-b/a

x1x2=c/a

对称轴x=-b/2a=-1

b/2a=1

b=2a

A(0,-3)

a=-3

顶点(-b/2a,b^2/4a-c)在x轴上

b^2/4a-c=0

b^2/4a=-3

b^2=-12a

b=2a,b^2=4a^2

a=-3,b=-6

y=-3x^2-6x-3