1. **Problem Statement:** Describe the transformations of the graph for the function $$y = -(x - 2)^2 - 4$$. 2. **General form and rules:** The parent function is $$y = x^2$$. - Horizontal shifts are determined by the value inside the parentheses with $$x$$: $$x - h$$ shifts right by $$h$$ units, $$x + h$$ shifts left by $$h$$ units. - Vertical shifts are added or subtracted outside the squared term. - A negative sign in front of the squared term reflects the graph over the x-axis (flips it). 3. **Analyze $$y = -(x - 2)^2 - 4$$:** - Horizontal shift: Since it is $$x - 2$$, the graph shifts right by 2 units. - Vertical shift: The $$-4$$ outside shifts the graph down by 4 units. - Flipped: The negative sign in front of the squared term means the graph is flipped (reflected) over the x-axis. 4. **Final transformations:** - Vertical Shift: Down 4 units - Horizontal Shift: Right 2 units - Flipped: Yes, reflected over the x-axis 1. **Problem Statement:** Describe the transformations of the graph for the function $$y = (x + 8)^2 + 3$$. 2. **Analyze $$y = (x + 8)^2 + 3$$:** - Horizontal shift: Since it is $$x + 8$$, the graph shifts left by 8 units. - Vertical shift: The $$+3$$ outside shifts the graph up by 3 units. - Flipped: There is no negative sign in front, so the graph is not flipped. 3. **Final transformations:** - Vertical Shift: Up 3 units - Horizontal Shift: Left 8 units - Flipped: No