The function given is $f(x) = x^2 + 5x - 8$, and you are asked to find $f(a + 1)$.

To do this, substitute $a + 1$ for $x$ in the function:

$f(a + 1) = (a + 1)^2 + 5(a + 1) - 8$

Now expand and simplify:

1. Expand $(a + 1)^2$: $(a + 1)^2 = a^2 + 2a + 1$

2. Expand $5(a + 1)$: $5(a + 1) = 5a + 5$

Now substitute both expansions into the expression for $f(a + 1)$:

$f(a + 1) = a^2 + 2a + 1 + 5a + 5 - 8$

Simplify:

$f(a + 1) = a^2 + (2a + 5a) + (1 + 5 - 8)$ $f(a + 1) = a^2 + 7a - 2$

Thus, $f(a + 1) = a^2 + 7a - 2$.

Would you like more details or have any questions?

Here are five related questions:

1. What is $f(2)$ for the function $f(x) = x^2 + 5x - 8$?
2. How does substituting $a - 1$ instead of $a + 1$ affect the outcome?
3. Can you graph $f(x) = x^2 + 5x - 8$?
4. What are the zeros (roots) of the function $f(x)$?
5. What is the derivative of $f(x) = x^2 + 5x - 8$?

Tip: When substituting expressions into a function, be careful to expand and simplify correctly to avoid errors.