Question

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

Explanation:

Step1: Identify the graph's shape

The graph on the right is a U - shaped curve, symmetric about the y - axis, with a vertex at the bottom. This is the characteristic shape of a parabola.

Step2: Match with the given equations

Among the given equations: \(y = mx + b\) is a straight line (linear), \(y=x^{2}\) is the equation of a parabola, \(y = x^{3}\) has a different cubic shape, and \(y=\vert x\vert\) has a V - shape. So the equation of the given graph should be \(y = x^{2}\).

Answer:

The equation of the non - linear graph (the parabola) is \(y=x^{2}\)