Wich inequality statement best represents the graph ? serious answers only!

a) f(x) ≤ -2x^2 + 4x

Step-by-step 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.

b. f(x) = –√x + 3this is the correct answer