Graph to Equation Puzzle: Identify the Matching Function

To solve this problem, let's examine each key feature of the graph:

• Step 1: Vertex and Direction - The graph appears to have its vertex at the origin and opens upwards.
• Step 2: Width - For a quadratic $y = ax^2$, if $|a| = 1$, the width is standard like $y = x^2$. In this graph, the parabola seems to follow the standard width.

Comparing to the options, we analyze for matching attributes:

• Choice 1: $y = 4x^2$ suggests a narrow upward parabola.
• Choice 2: $y = 2x^2$ is narrower than a standard parabola.
• Choice 3: $y = x^2$ matches a standard parabola.
• Choice 4: $y = -x^2$ opens downward.

Given the graph opens upwards and matches the standard parabola, the correct equation is $y = x^2$.