To graph the function \( f(x) = -\frac{1}{2}(x+2)^2 - 1 \), we can follow these steps:
Step 1: Identify the Vertex
The function is in the vertex form \( f(x) = a(x-h)^2 + k \), where \((h, k)\) is the vertex.
From the function:
- \( a = -\frac{1}{2} \)
- \( h = -2 \)
- \( k = -1 \)
Thus, the vertex is at the point \((-2, -1)\).
Step 2: Plot the Vertex
You would plot the vertex point \((-2, -1)\) on your graph.
Step 3: Find Another Point on the Parabola
To find another point, we can substitute a value for \( x \) into the function. Let's choose \( x = 0 \):
\[ f(0) = -\frac{1}{2}(0 + 2)^2 - 1 \] \[ = -\frac{1}{2}(2)^2 - 1 \] \[ = -\frac{1}{2}(4) - 1 \] \[ = -2 - 1 = -3 \]
So, the point \((0, -3)\) is also on the parabola.
Step 4: Plot the Other Point
You would plot the point \((0, -3)\) on the graph.
Step 5: Draw the Parabola
Now, draw the parabola opening downwards, passing through the vertex \((-2, -1)\) and the point \((0, -3)\). The parabola will be symmetric about the vertical line through the vertex.
Summary of Points
- Vertex: \((-2, -1)\)
- Another point: \((0, -3)\)
Axis Range
Make sure your x-axis ranges from 0 to -10 and your y-axis from 0 to -10, to appropriately display both points.
If you have further questions or need help visualizing the graph, please let me know!
1 answer