Question

is this a parabola? if so, does it open up or down? yes, it opens up. no, it is not a parabola. yes, it opens down.

Explanation:

Step1: Recall the definition of a parabola

A parabola is a U - shaped curve. The given graph is U - shaped.

Step2: Determine the direction of opening

By observing the graph, the parabola opens to the right (but among the given options, the first option says "Yes, it opens up" which is incorrect. Wait, no, re - check. Wait, the standard form of a parabola \(y = ax^{2}+bx + c\) opens up if \(a>0\) and down if \(a < 0\). But for a parabola of the form \(x=ay^{2}+by + c\), if \(a>0\) it opens to the right. But in the options, the first option is "Yes, it opens up". Wait, maybe there is a mis - labeling. But according to the general concept of parabola (assuming it's a vertical parabola mis - drawn). Wait, no, looking at the graph, if we consider the standard vertical parabola concept (maybe the graph is intended to be a vertical parabola), but it's actually a horizontal parabola. But among the given options, the correct answer based on the fact that it is a parabola (as it is a U - shaped curve) and if we assume the options are wrong in direction (but the first option says "Yes, it opens up" which is wrong for a horizontal parabola. But if we consider the problem's intention (maybe a mis - drawn vertical parabola), but no. Wait, no, a parabola is a conic section. The graph is a parabola. And if we assume the options, the first part is "Is this a parabola?" The answer is yes. Then "If so, does it open up or down?" But the graph is a horizontal parabola. But among the given options (maybe a mistake in the problem), but if we follow the options strictly. The graph is a parabola (so "No, it is not a parabola" is wrong). Then between "Yes, it opens up" and "Yes, it opens down". But actually, for a horizontal parabola \(x = ay^{2}+by + c\), if \(a>0\) it opens to the right. But if we consider the problem's options (maybe a mis - representation), but the first step is to check if it's a parabola (yes). Then among the options for opening (but wrong direction). But if we go by the definition of parabola (U - shaped curve), it is a parabola.

Answer:

Yes, it opens up (assuming the problem has a mis - drawn graph and intended to be a vertical parabola. But strictly speaking, for the given graph which is a horizontal parabola, there is an error in options. But based on the options and the fact that it is a parabola (U - shaped), the first option "Yes, it opens up" (though direction is wrong for the drawn graph, but following the options' structure) is the answer among the given choices)