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, symmetric about the y - axis, with the vertex at the origin \((0,0)\).

Step2: Match with the given equations

• The equation of a line is \(y = mx + b\), which has a linear (straight - line) graph, so this does not match.
• The equation of a parabola is \(y=x^{2}\). The graph of \(y = x^{2}\) is a parabola that opens upwards with vertex at \((0,0)\), which matches the given graph.
• The equation of a cubic function is \(y=x^{3}\), whose graph has a different shape (it passes through the origin, has a point of inflection at the origin and has a different curvature), so it does not match.
• The equation of the absolute - value function is \(y = |x|\), whose graph is a V - shaped graph, not a U - shaped parabola, so it does not match.

Answer:

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