Answer:
You did not write the options, but let's solve it in a general way.
f(x) and g(x) are quadratic functions, this means that:
f(x) = a*x^2 + b*x + c
g(x) = d*x^2 + e*x + f
now, (g + f)(x) is a linear function that goes trough the points (-3, 4), (0,1 ) and (1,0)
(g + f)(x) = s*x + k
We can find the slope of this linear function as:
S = (y2 - y1)/(x2 - x1)
i will use the first two points.
S = (1 - 4)/(0 - (-3) = -3/3 = -1
so we have: ( f + h)(x) = -1*x + k
and we can find k using one of the points, for example (0, 1)
1 = -1*0 + k
b = 1.
so we have: (f + g)(x) = -1*x + 1.
Now, (f+g)(x) = (a + d)*x^2 + (b + e)*x + (c + f) = -1*x + 1.
So we must have that:
a = -d
b + e = -1
c + f = 1.
