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The task requires finding a quadratic regression curve that fits the given points: \((0, 0)\), \((-3, 3)\), \((2, 2)\), and \((-5, 5)\). The equation of a quadratic function is generally:

\[
y(x) = ax^2 + bx + c
\]

To find the coefficients \(a\), \(b\), and \(c\), I will use quadratic regression. Let me calculate it.The quadratic regression equation that fits the given points \((0, 0)\), \((-3, 3)\), \((2, 2)\), and \((-5, 5)\) is:

\[
y(x) = 0.2x^2 + 0.0828x + 0.7241
\]

Would you like further details or have any questions?

Here are 5 related questions for practice:
1. How would the regression change if another point was added to the dataset?
2. How does the least squares method find the best-fitting quadratic curve?
3. Can quadratic regression be applied to non-parabolic datasets effectively?
4. How do outliers affect the accuracy of quadratic regression?
5. What are the differences between linear and quadratic regression?

**Tip:** Always ensure that your dataset is appropriate for quadratic modeling before applying quadratic regression. If the data isn't parabolic, consider alternative models.

Use technology to find the quadratic regression curve through the given points: (0, 0), (-3, 3), (2, 2), (-5, 5). Round all coefficients to four decimal places.

Find the quadratic regression curve through the points (0, 0), (-3, 3), (2, 2), (-5, 5). Learn how to compute this using the least squares method, rounding coefficients to four decimal places.

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