The problem provides the equation $y = x^2 - K$ and a table of $x$ and $y$ values that satisfy this equation. The goal is to find the value of $K$. The problem asks to identify what K represents and find its value using the table.

1. Problem Description

The problem provides the equation $y = x^2 - K$ and a table of $x$ and $y$ values that satisfy this equation. The goal is to find the value of $K$. The problem asks to identify what K represents and find its value using the table.

2. Solution Steps

We can use any pair of $x$ and $y$ values from the table to solve for $K$. Let's use the point $(x, y) = (-3, 5)$. Substituting these values into the equation $y = x^2 - K$, we get:

$5 = (-3)^2 - K$

$5 = 9 - K$

$K = 9 - 5$

$K = 4$

Now, let's use the point $(x, y) = (-2, 0)$ to verify our answer:

$0 = (-2)^2 - K$

$0 = 4 - K$

$K = 4$

The value of K is consistent across different points from the table. K represents the minimum value (vertex) of the parabola.

3. Final Answer

The value of K is

4.