Question

已知函数f(x)=ax^2十bX十c的图象在y轴上的截距是1,且f(x+1)=f(X)+x+1求:1f(x)的解析式.2

Answer 1

f(0) = 1,so c = 1

f(x+1) = a(x+1)^2 + b(x+1) + c = ax^2 + bx + c + x+1

so 2a + b = b+1,a = 1/2

b+a+c = c+1

b = 1/2

f(x) = 1/2 x^2 + 1/2 x + 1