Hi there!
We can find the range using completing the square:
y = -x² - 2x + 8
Factor out a -1:
y = -(x² + 2x) + 8
Use the first two terms. Take the second term's coefficient, divide by 2, and square:
y = -(x² + 2x + 1) + 8
Remember to add by 1 because we cannot randomly add an additional number into the equation:
y = -(x² + 2x + 1) + 8 + 1
Simplify:
y = -(x + 1)² + 9
Since the graph opens downward (negative coefficient), the range is (-∞, 9)