To solve this problem, we need to perform a quadratic regression on the given data points to find the quadratic function of the form $y = ax^2 + bx + c$, where $a$, $b$, and $c$ are coefficients that need to be determined. The data points provided are:

Using a calculator with a quadratic regression function (or statistical software), input the $x$ and $y$ values to find the coefficients $a$, $b$, and $c$ for the quadratic equation.

The steps on most calculators are as follows:

1. Enter the data points under the regression menu.
2. Choose quadratic regression.
3. The calculator will output the coefficients $a$, $b$, and $c$.

Would you like to proceed with calculating the regression manually using the provided data, or do you have access to a calculator that can perform this regression for you?

Here are five related questions to deepen your understanding:

1. How does quadratic regression differ from linear regression in terms of modeling data?
2. Why is a quadratic model appropriate for modeling the path of a projectile?
3. Can you predict the time when the projectile will hit the ground using this quadratic equation?
4. How does changing the coefficient $a$ affect the shape of the parabola?
5. What other real-world scenarios can be modeled using quadratic functions?

Tip: In a quadratic equation $y = ax^2 + bx + c$, if $a$ is positive, the parabola opens upward. If $a$ is negative, the parabola opens downward.