To determine the axis of symmetry for the function $f(x) = 5(x + 1)^2 - 8$, we need to recognize that this is a quadratic function in the vertex form:

$f(x) = a(x - h)^2 + k$

where $(h, k)$ is the vertex of the parabola, and the axis of symmetry is the vertical line $x = h$.

In this case:

• The function $f(x) = 5(x + 1)^2 - 8$ is in the form $a(x - h)^2 + k$ with $h = -1$ and $k = -8$.
• Thus, the axis of symmetry is given by the line $x = -1$.

Answer:

The axis of symmetry for the function $f(x) = 5(x + 1)^2 - 8$ is $x = -1$.

Would you like further details on this solution or have any questions?

Here are some related questions to deepen your understanding:

1. How do we determine the vertex of a quadratic function in standard form?
2. What effect does the coefficient $a$ have on the shape of a parabola?
3. How can we find the axis of symmetry if a quadratic function is given in standard form $ax^2 + bx + c$?
4. Why does the function $f(x) = 5(x + 1)^2 - 8$ open upwards?
5. How can we identify if a parabola has a minimum or maximum value?

Tip: When working with quadratic functions in vertex form, the $h$ value directly gives the axis of symmetry.