Question

non-linear graphs
graphs
line: y = mx + b
parabola: y = x²
cubic : y = x³
absolute value y = |x|

Explanation:

Step1: Identify the graph shape

The given graph is a U - shaped curve, which is the characteristic shape of a parabola.

Step2: Match with the given equations

Among the given equations, the equation for a parabola is \(y = x^{2}\). We can check the key features: the vertex of \(y=x^{2}\) is at \((0,0)\) and it opens upwards, which matches the graph shown (vertex at or near the origin and opening upwards). The line \(y = mx + b\) is a straight line, the cubic \(y=x^{3}\) has a different S - shaped curve, and the absolute value \(y = |x|\) has a V - shape, so they do not match.

Answer:

The graph represents the parabola \(y=x^{2}\)