To find the quadratic regression curve through the given points, we need to use the general form of a quadratic equation:

$y(x) = ax^2 + bx + c$

We will use quadratic regression techniques to fit the curve to the given points $(0, -2)$, $(-3, 1)$, $(2, 0)$, and $(-5, 3)$. The coefficients $a$, $b$, and $c$ are determined by minimizing the sum of the squared differences between the predicted values and the actual values.

I'll compute the quadratic regression for you to find $a$, $b$, and $c$.The quadratic regression curve that fits the given points is:

$y(x) = 0.2000x^2 + 0.0828x - 1.2759$

Would you like further details on how this was calculated or have any questions?

Here are 5 related questions you can explore:

1. How is the quadratic regression different from linear regression?
2. What are the steps to perform quadratic regression manually?
3. How do residuals affect the accuracy of the regression model?
4. Can quadratic regression be applied to a larger data set?
5. How can outliers affect the quadratic regression curve?

Tip: When using quadratic regression, ensure that the data set shows a curved pattern; otherwise, a linear model might be more appropriate.