Hello, fabxx!
That is a terrible graph!
. . And not a "neat" problem either . . .
The figure below shows the graph of a quadratic function $\displaystyle h(x)$
whose maximum value is $\displaystyle h(2).$
If $\displaystyle h(a)=0$, which of the following could be the value of $\displaystyle a$?
. . $\displaystyle (a)\;\text{}1 \qquad (b)\;0 \qquad (c)\;2\qquad (d)\;3 \qquad (e)\;4$ Code:

 *
 * : *
* : *
* : *
 :
*++*
 2

*  *

The quadratic function is a downopening parabola.
Its maximum (vertex) is at: .(2, h(2))
If $\displaystyle h(a) = 0$, we are seeking the xintercepts of the graph.
One is to the left of the origin (negative)
. . the other is to the right of $\displaystyle x = 2.$
We know that the two intercepts are symmetric
. . about the axis of symmetry, $\displaystyle x = 2.$
Since the left intercept is negative, it is more than 2 units to the left of $\displaystyle x = 2.$
Then the right intercept is more than 2 units to the right of $\displaystyle x = 2.$
. . Hence: .$\displaystyle a > 4$
Among the given choices, the only one is: .$\displaystyle a = \text{}1$ . . . answer (a)