Does the point (–2, –6) satisfy the equation y = –2x2 − –2?

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 \( y = -2x^2 + 2 \).