Math Challenge please answer huhuhuhu

Question

if f(x)=ax^2 + bx + c and

f(x+3)=x^2 + 7x + 4 , what is a, b and c ?

Answer 1

If ax2 + bx + c = f(x) then f(x+3) = a(x+3)² +b(x+3) + c = ax² + 6ax + 9a + bx + 3b + c

Collecting terms, we have ax² + (6a + b)x + (3b + c) this must equal x² + 7x + 4

So, a = 1, (by inspection)

6a + b = 7, so, b = 1

3b +c = 4, so, c = 1