To determine if the point (–2, –6) satisfies the equation \( y = -2x^2 - -2 \), we need to substitute \( x = -2 \) into the equation and see if we get \( y = -6 \).
First, we simplify the equation:
\[ y = -2x^2 + 2 \]
Now, substitute \( x = -2 \):
\[ y = -2(-2)^2 + 2 \]
Calculating \( (-2)^2 \):
\[ (-2)^2 = 4 \]
Now substituting back into the equation:
\[ y = -2(4) + 2 \]
Calculating:
\[ y = -8 + 2 = -6 \]
Since we have \( y = -6 \), and this matches the \( y \)-coordinate of the point (–2, –6), we conclude that the point (–2, –6) does satisfy the equation \( y = -2x^2 + 2 \).