https://file.aiquickdraw.com/mathbot/file/17290911620975q0fxtbk.jpg

From the graph provided, we can observe the following important points:

1. The graph is a parabola opening upwards, indicating the equation is a quadratic function.
2. The x-intercepts (roots) of the parabola are \(-6\) and \(0\), as it crosses the x-axis at these points.
3. The vertex of the parabola appears to be at \((-3, -9)\), which is the minimum point.

Given that the x-intercepts are \(-6\) and \(0\), we can write the factored form of the quadratic equation as:

\[
y = a(x + 6)(x)
\]

To find the value of \(a\), we use the vertex point \((-3, -9)\) and substitute it into the equation:

\[
-9 = a(-3 + 6)(-3)
\]
\[
-9 = a(3)(-3)
\]
\[
-9 = -9a
\]
\[
a = 1
\]

Therefore, the equation in factored form is:

\[
y = (x + 6)(x)
\]

This simplifies to:

\[
y = x(x + 6) = x^2 + 6x
\]

Would you like further explanation or details?

### Related Questions:
1. How can I convert a factored form equation into standard form?
2. What are the general steps to derive the equation of a parabola from a graph?
3. How do you determine the direction a parabola opens based on its equation?
4. What is the significance of the vertex in a quadratic function?
5. How can I find the axis of symmetry for a parabola from its equation?

**Tip:** The coefficient \(a\) in a quadratic equation \(y = ax^2 + bx + c\) determines the "width" and direction of the parabola's opening.

Use the graph of the function to write the equation in factored form.

Learn how to factor quadratic equations using the graph of the function. In this example, the parabola intersects the x-axis at -6 and 0, and the vertex is at (-3, -9). This walkthrough covers writing the equation in factored form and solving for 'a'. Suitable for students in Grades 9-10.

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