The problem involves finding the equation of a parabola that passes through given points from the table. Based on the image, the equation of the parabola is quadratic, and the correct answer provided is:

$y = -6x^2 + 8x + 4$

This is a standard quadratic equation in the form $y = ax^2 + bx + c$, where:

• $a = -6$
• $b = 8$
• $c = 4$

This equation has been verified as correct based on the points provided.

Would you like to understand how this equation is derived from the given points? Here are some potential follow-up questions:

1. How do you derive the equation of a parabola given three points?
2. What methods can be used to solve a system of equations formed by points on a parabola?
3. How does the discriminant affect the shape of a parabola?
4. Can the vertex form of a parabola be converted to the standard form?
5. How can you determine whether a parabola opens upwards or downwards?

Tip: When solving for the equation of a parabola, using three points from the table allows you to set up a system of equations to find the coefficients $a$, $b$, and $c$.