Question

抛物线顶点（1,16）,且抛物线与x轴的两交点相距8.求此二次函数的解析式.

Answer 1

设y=a(x-1)²+16

=ax ²-2ax+a+16

x1+x2=2,x1x2=(a+16)/a

x1 ²+x2 ²=(x1+x2) ²-2x1x2=4- 2(a+16)/a

|x1-x2|=8

x1 ²-2x1x2+x2 ²=64

4- 2(a+16)/a-2(a+16)/a=64

-4(a+16)/a=60

-4a-64=60a

a=-1

故y=-x ²+2x+15