Question

if f(x) and g(x) are a quadratic function but (f + g)(x) produce the graph below, which statement must be true

Answer 1

The leading coefficients are opposites.

For instance
f(x) = 2x^2 + 5x + 6
g(x) = -2x^2 + 8x - 3
here the leading coefficients 2 and -2 are opposites

Adding function f(x) and g(x) gets us
f(x) + g(x) = (2x^2+5x+6) + (-2x^2+8x-3)
f(x) + g(x) = (2x^2-2x^2) + (5x+8x) + (6-3)
f(x) + g(x) = 0x^2 + 13x + 3
f(x) + g(x) = 13x + 3

The two quadratics add up to a linear equation