What is an equation for the quadratic function represented by the table shown? f(x) = _____ (x – _____)² + _____.

To determine the equation of a quadratic function from a table, we often look for the vertex form of a quadratic, which is given by:

f(x) = a(x – h)² + k,

where (h, k) is the vertex of the parabola.

1. Find the vertex: From the table, identify the maximum or minimum point. The x-value where this occurs will be your h, and the corresponding f(x) value will be your k.

2. Determine ‘a’: Choose another point from the table (x, f(x)). Use this point to solve for ‘a’ by substituting h and k into the vertex form.

3. Write the equation: Plug h, k, and a into the vertex form.

If you can provide values from the table, I can help you through this step-by-step process to find your specific quadratic function!