$$ f(x)=-(x+1)^{2}+2 $$ Make sure that you graph the vertex, the AOS, the 2 extra points and refelect them across the AOS.

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1. **Identify the vertex form of the parabola**

The given function is  
   $$
   f(x)=-(x+1)^2+2.
   $$  
   It is already in vertex form, $$ f(x)=a(x-h)^2+k $$, where  
   $$
   a=-1,\quad h=-1,\quad k=2.
   $$

2. **Determine the vertex**

The vertex is at  
   $$
   (h, k)=(-1, 2).
   $$

3. **Find the Axis of Symmetry (AOS)**

The axis of symmetry is the vertical line passing through the vertex, so it is  
   $$
   x=-1.
   $$

4. **Find 2 extra points on one side and reflect them across the AOS**

We'll start by choosing two $$x$$-values on one side of the AOS. For convenience, let’s choose values to the right of $$x=-1$$.

- **Extra Point 1: Using $$x=0$$**  
     
     Evaluate $$ f(0) $$:  
     $$
     f(0)=-(0+1)^2+2= -1+2=1.
     $$  
     This gives the point  
     $$
     (0, 1).
     $$
     
     *Reflect across the AOS:*  
     The reflection of a point $$(x, y)$$ across the line $$x=-1$$ is  
     $$
     (x', y) \quad \text{where} \quad x' = -1 - (x - (-1)) = -1 - (x+1).
     $$  
     For $$(0, 1)$$,  
     $$
     x' = -1 - (0+1) = -2.
     $$  
     So the reflected point is  
     $$
     (-2, 1).
     $$

- **Extra Point 2: Using $$x=1$$**  
     
     Evaluate $$ f(1) $$:  
     $$
     f(1)=-(1+1)^2+2= -4+2=-2.
     $$  
     This gives the point  
     $$
     (1, -2).
     $$
     
     *Reflect across the AOS:*  
     For $$(1, -2)$$,  
     $$
     x' = -1 - (1+1) = -1 - 2 = -3.
     $$  
     So the reflected point is  
     $$
     (-3, -2).
     $$

5. **Summary of the key points for the graph**

- **Vertex:** $$\,(-1, 2)$$
   - **Axis of Symmetry (AOS):** $$\,x=-1$$
   - **Extra Points and their Reflections:**  
     - Point: $$(0, 1)$$ and its reflection: $$(-2, 1)$$  
     - Point: $$(1, -2)$$ and its reflection: $$(-3, -2)$$

Plot these points on the coordinate plane and draw a smooth parabolic curve opening downward (since $$a=-1$$). Mark the vertex, draw the vertical line $$x=-1$$ to indicate the axis of symmetry, and ensure the extra points are plotted along with their reflections across the AOS.
To graph the function $$ f(x) = -(x+1)^2 + 2 $$, follow these steps: 1. **Vertex**: $$(-1, 2)$$ 2. **Axis of Symmetry (AOS)**: $$x = -1$$ 3. **Extra Points**: - $$(0, 1)$$ and its reflection $$(-2, 1)$$ - $$(1, -2)$$ and its reflection $$(-3, -2)$$ Plot these points and draw the parabola opening downward with the vertex at $$(-1, 2)$$ and the AOS at $$x = -1$$.

\( f(x)=-(x+1)^{2}+2 \) Make sure that you graph the vertex, the AOS, the 2 extra points and refelect them across the AOS.

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