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