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.