To find the vertex and axis of symmetry for the quadratic function $f(x) = - (x + 3)^2 + 8$, we can analyze its standard form.

Vertex

The function is in vertex form $f(x) = a(x - h)^2 + k$, where $(h, k)$ is the vertex. Here, we can see:

• $a = -1$
• $h = -3$
• $k = 8$

Thus, the vertex is: $(-3, 8)$

Axis of Symmetry

The axis of symmetry for a parabola in this form is given by the line $x = h$. Therefore, the axis of symmetry is: $x = -3$

Summary

• Vertex: $(-3, 8)$
• Axis of Symmetry: $x = -3$

Do you want details or have any questions? Here are some related questions you might consider:

1. How can you graph the function $f(x)$?
2. What are the intercepts of the function?
3. How does the value of $a$ affect the parabola's direction?
4. Can you convert this function into standard form?
5. What is the maximum or minimum value of the function?

Tip: To understand the properties of quadratics better, practice transforming between different forms (vertex, standard, and factored).