To determine if the point (2, –7) satisfies the equation \( y = -2x^2 - 8 \), we can substitute the \( x \) value from the point into the equation and see if we get the corresponding \( y \) value.
The point is \( (2, -7) \), so we have:
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Substitute \( x = 2 \) into the equation: \[ y = -2(2)^2 - 8 \] Simplify it: \[ y = -2(4) - 8 \] \[ y = -8 - 8 \] \[ y = -16 \]
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Now we compare the calculated \( y \) value with the \( y \) coordinate of the point:
- The calculated \( y \) value is \( -16 \)
- The \( y \) coordinate from the point (2, -7) is \( -7 \)
Since \(-16 \neq -7\), the point (2, –7) does not satisfy the equation \( y = -2x^2 - 8 \).