For example, if we know that the quadratic function f (x) satisfies f (x + 1) - f (x) = 2x, f (0) = 1, we can find the analytic expression of F (x) | Math enthusiast | Mathematical art

For example, if we know that the quadratic function f (x) satisfies f (x + 1) - f (x) = 2x, f (0) = 1, we can find the analytic expression of F (x)

f(x)=ax²+bx+c
f(0)=0+0+c=1
c=1
f(x+1)-f(x)=2x
a(x+1)²+b(x+1)+c-ax²-bx-c=2x
2ax+a+b=2x
So 2A = 2
a+b=0
So a = 1, B = - 1
f(x)=x²-x+1
Where are you from, kid?

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