https://file.aiquickdraw.com/mathbot/file/1726658570622x7rbhq4g.jpg

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.

Select the equation which best describes the graph shown below (parabola opening upwards with vertex at origin).

This problem helps students identify the equation of a parabola from a graph, focusing on quadratic functions. The graph shows a parabola with a vertex at the origin, corresponding to y = x^2. Suitable for Grades 7-9.

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