To evaluate g(-3) = -x^2 + 6x - 2, substitute -3 for x in the equation:
g(-3) = -(-3)^2 + 6(-3) - 2
Simplify the equation by following the order of operations:
g(-3) = -9 + (-18) - 2
Then, perform the addition and subtraction:
g(-3) = -9 - 18 - 2
Finally, calculate the result:
g(-3) = -29