Answer: y ≤ 7
Interval notation is: (-∞, 7]
Explanation:
First, remember that range represents the y-values of the function.
-(x + 3)² + 7 is in vertex form: a(x - h)² + k where
- (h, k) is the vertex
- a is negative so it is reflected across the x-axis (upside-down parabola)
Therefore, the parabola has a maximum y-value at k (which is 7) and continues downward to negative infinity. ⇒ Range: y ≤ 7