The equation for the quadratic graph provided can be written as:

\[
y = -\frac{2}{3}(x + 3)(x + 1)
\]

This is based on the given x-intercepts \((-3, 0)\) and \((-1, 0)\), and the y-intercept \((0, -2)\). If expanded, the equation is:

\[
y = -\frac{2}{3}x^2 - \frac{8}{3}x - 2
\]

This equation represents the quadratic curve shown in the graph.

Do you need any further explanations or help with anything else?

### Related Questions:
1. How do you derive the vertex form of a quadratic equation from its standard form?
2. What is the relationship between the discriminant and the number of real roots in a quadratic equation?
3. How does changing the coefficient \(a\) affect the shape of the parabola?
4. What are the steps to graph a quadratic function from its equation?
5. How do you find the axis of symmetry for a quadratic equation?
6. How can you determine the maximum or minimum value of a quadratic function?
7. What is the significance of the y-intercept in the context of a quadratic function?
8. How does the factorization of a quadratic equation help in solving it?

### Tip:
When graphing a quadratic equation, it helps to plot the vertex, axis of symmetry, x-intercepts, and y-intercept first to ensure accuracy.

Learn how to write the equation for a quadratic graph with given x-intercepts and y-intercept. Detailed step-by-step solution provided. Suitable for students in Grades 9-12.

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