https://file.aiquickdraw.com/mathbot/file/17246989602480otyly2n.jpg

To determine the quadratic function depicted in the graph, let's analyze the key features of the parabola:

1. **Vertex**: The graph shows that the vertex of the parabola is at the origin (0, 0).
2. **Direction**: The parabola opens upwards, which means the coefficient of the \(x^2\) term is positive.
3. **Points on the Graph**: It appears that the parabola passes through points \((0,0)\), \((1, 4)\), and \((-1, 4)\).

Given that the vertex form of a parabola is \(y = a(x - h)^2 + k\), where \((h, k)\) is the vertex, and here \((h, k) = (0, 0)\), the equation simplifies to:

\[
y = ax^2
\]

To find the value of \(a\), use the point \((1, 4)\):

\[
4 = a(1)^2 \implies a = 4
\]

Thus, the quadratic function for this parabola is:

\[
y = 4x^2
\]

### Would you like to explore further or have any questions?

Here are some related questions:
1. What is the effect of changing the value of \(a\) in the quadratic function \(y = ax^2\)?
2. How do you determine if a parabola opens upwards or downwards based on its equation?
3. What are the key differences between the vertex form and standard form of a quadratic equation?
4. How can you find the x-intercepts of a parabola from its quadratic function?
5. How does the vertex form help in easily identifying the vertex of a parabola?

**Tip:** To quickly determine the equation of a parabola from a graph, identify the vertex and another point on the parabola to solve for the coefficient \(a\).

Explore the quadratic formula applied to a specific problem involving a parabolic graph. Learn how to determine the quadratic function from given graph points and vertex characteristics. Suitable for students in Grades 7-9.

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