https://file.aiquickdraw.com/mathbot/file/1726621990030s6s0u5mz.jpg

You have uploaded a worksheet showing a quadratic function in vertex form: 

\[
f(x) = -3(x + 7)^2 + 6
\]

The task is to identify the parameters \(a\), \(h\), and \(k\), and the vertex of the parabola.

1. **The equation** is in vertex form:
   \[
   f(x) = a(x - h)^2 + k
   \]
   - \(a\) controls the direction and width of the parabola.
   - \(h\) is the x-coordinate of the vertex (note the sign change from the equation).
   - \(k\) is the y-coordinate of the vertex.

### From the given equation:
- \(a = -3\) (which is already filled in).
- \(h = -7\) (since \(x + 7\) means \(h = -7\)).
- \(k = 6\).

### Vertex:
The vertex is \((h, k) = (-7, 6)\).

### Summary:
- \(a = -3\)
- \(h = -7\)
- \(k = 6\)
- Vertex: \((-7, 6)\)

Would you like more details on how to plot the graph or further explanation? 

Here are five related questions:
1. How does the value of \(a\) affect the shape and direction of the parabola?
2. How would the vertex change if the equation was \(f(x) = -3(x - 7)^2 + 6\)?
3. What is the axis of symmetry for this parabola?
4. How can you find the x-intercepts of the quadratic function?
5. How would you rewrite this equation in standard form?

**Tip:** The value of \(h\) is always the opposite of what appears in the equation, while \(k\) remains the same.

Identify the values of a, h, k, and the vertex of the quadratic function f(x) = -3(x + 7)^2 + 6.

Learn how to find the values of a, h, k, and the vertex of the quadratic function f(x) = -3(x + 7)^2 + 6. This problem covers key concepts in algebra, including the vertex form of a parabola and how to determine the vertex of the function.

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