https://file.aiquickdraw.com/mathbot/file/1727115704038e95qq5nu.jpg

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 \(c\).

Write an equation of the parabola that passes through the points: (-8, -444), (-5, -186), (1, 6), (2, -4), (6, -164).

Learn how to find the equation of a parabola that passes through given points: (-8, -444), (-5, -186), (1, 6), (2, -4), (6, -164). This problem demonstrates key algebraic concepts, such as quadratic equations and solving systems of equations, suitable for Grades 10-12.

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