已知抛物线过A(-1,0)和(3,0)两点,与y轴交于点C,且BC=3倍根号2,则这条抛物线的解析式为?

y=ax^2+bx+c
过A(-1,0)和(3,0)两点
y=a(x+1)(x-3)
BC=3√2,与y轴交于点C,X=0
B(3,0)C(0,C)
3^2+C^2=18
C=±3
X=0
±3=a(0+1)(0-3)
a=-1a=1
抛物线的解析式为:
y=x^2-2x-3
或 y=-x^2+2x+3