Answer: a) f(x) ≤ -2x^2 + 4x
Explanation:
In the graph you can see that the "hands" of the quadratic function go up, this means that the principal constant (the one that multiplicates the square term) is positive:
this is:
for a function f(x) = a*x^2+ b*x + c
if a is positive, the hands will go upside, if a is negative, the hands will go downside.
we also can see that the shaded area is upside the curve, so we are looking for f(x) > something.
Then we can discard the third option because we have f > -2*x^2..
the remaining options are:
a) f(x) ≤ -2x^2 + 4x or f(x) ≥ 2x^2 - 4x
b) f(x) ≥ 2x^2 + 4x
first, you can see that in the second function both terms have the same sign, so there can be only one x-intercept, but in the graph, we can see two x-intercepts, so we can also discard option b.
The remaining option, and the correct one, is option a.