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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.

Evaluate the function for the indicated value: f(x) = x^2 + 5x - 8; find f(a + 1).

Learn how to evaluate the quadratic function f(x) = x^2 + 5x - 8 by substituting a + 1 for x. Step-by-step explanation of expanding and simplifying the expression.

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