The graph shown in the image depicts a parabola that opens upwards with its vertex at the origin (0,0). This is the characteristic shape of the equation $y = x^2$, which matches a standard quadratic function.

Let's evaluate the options:

1. $y^2 = x$ – This represents a sideways parabola, which is not correct here.
2. $y = x$ – This is a straight line, so it doesn't match the parabola.
3. $y = x^2$ – This describes a parabola opening upwards, matching the graph.
4. $y = x + 2$ – This is the equation of a line, not a parabola.

Thus, the correct answer is $y = x^2$.

Would you like more details or explanations?

Here are 5 related questions you might find helpful:

1. What is the general form of a quadratic equation?
2. How can you determine the vertex of a parabola from its equation?
3. How does the coefficient of $x^2$ affect the width of a parabola?
4. What transformations affect the position and shape of a parabola?
5. How does a horizontal shift of a parabola affect its equation?

Tip: When dealing with quadratic functions, always look for key features like the vertex, direction of opening, and axis of symmetry to help identify the correct equation.