二次函数f(x)满足f(x+1)-f(x)=2x+3且f(0)=2求f(x)解释试

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二次函数f(x)满足f(x+1)-f(x)=2x+3且f(0)=2求f(x)解释试
二次函数f(x)满足f(x+1)-f(x)=2x+3且f(0)=2求f(x)解释试

二次函数f(x)满足f(x+1)-f(x)=2x+3且f(0)=2求f(x)解释试
f(x) = ax² + bx + c,f(0) = c = 2f(x+ 1) = a(x + 1)² + b(x+ 1) + cf(x + 1) - f(x) = a[(x + 1) + x][(x + 1) - x]+b(x + 1 - x) = a(2x + 1) + b = 2ax + a + b = 2x + 32a = 2,a = 1,a + b = 3,b = 2f(x) = x² + 2x + 2