Find the quadratic function f(1) =-7 f(3)=-19 and f(3)= -49

Since problem says the function is quadratic, it must be a function, except that there is a typo: one of the f(3) must read f(-3).
Assuming the last f(3) should read f(-3), then the data now read:
f(1) =-7 f(3)=-19 and f(-3)= -49
The general quadratic is 
f(x)=ax^2+bx+c
f(1)=-7 => a+b+c=-7(1)
f(3)=-19 => 9a+3b+c=-19(2)
f(-3)=-49 => 9a-3b+c=-49(3)
(2)-(3)
6b=30 => b=5
(2)-(1)
8a+2b=-12 => 8a+10=-12 => a=(-22/8)=-2.75
substitute a and b in (1)
-2.75+5+c=-7 => c=-9.25
=> quadratic is
-2.75x^2+5x-9.25=0  for f(1) =-7 f(3)=-19 and f(-3)= -49

If the typo is not as assumed above, proceed similarly to get
f(x)=-4x^2-5x+2    for f(1) =-7 f(-3)=-19 and f(3)= -49

What mathematical statement is missing ? ? the answer is b