Final answer:
The given function, h(x) = -1/2 (x+1)² - 4, represents a narrower downward-opening parabola that is translated 4 units down from the original parent function.
Step-by-step explanation:
The given function is h(x) = -1/2 (x+1)² - 4.
To describe the transformation and graph of this function, we can analyze the equation.
- The factor -1/2 in front of (x+1)² means that the graph will be reflected in the x-axis and horizontally compressed, resulting in a narrower parabola.
- The term -4 shifts the graph downwards 4 units.
Combining these transformations, the graph of the function will be a narrower downward-opening parabola translated 4 units down from the original parent function.