It is known that the quadratic function f (x) satisfies the following conditions: (1) the axis of symmetry is x = 1; (2) the maximum value is 15; (3) the sum of two squares of F (x) = 0 is 7 For example, find the analytic expression of F (x)

y=a(x-1)²+15
=ax²-2ax+a+15
x1+x2=2
x1x2=(a+15)/a
x1²+x2²=(x1+x2)²-2x1x2=4-2(a+15)/a=7
2(a+15)/a=-3
2(a+15)=-3a
a=-6
y=-6a(x-1)²+15

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