Given the function $f(x) = x^2 + 7x + 8$, let's solve each part:

(a) $f(0)$:

$f(0) = 0^2 + 7(0) + 8 = 8$

(b) $f(1)$:

$f(1) = 1^2 + 7(1) + 8 = 1 + 7 + 8 = 16$

(c) $f(-1)$:

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

(d) $f(-3)$:

$f(-3) = (-3)^2 + 7(-3) + 8 = 9 - 21 + 8 = -4$

(e) $f(a)$ (in terms of $a$):

$f(a) = a^2 + 7a + 8$

(f) $f(x + h)$ (in terms of $x + h$):

$f(x + h) = (x + h)^2 + 7(x + h) + 8$ Expand this: $f(x + h) = (x^2 + 2xh + h^2) + 7(x + h) + 8$ $f(x + h) = x^2 + 2xh + h^2 + 7x + 7h + 8$ So, $f(x + h) = x^2 + 7x + 2xh + h^2 + 7h + 8$

Would you like further details or clarifications?

Here are some related questions:

1. What happens if $x$ is negative in $f(x)$?
2. How would the vertex form of $f(x)$ look like?
3. What is the derivative of $f(x) = x^2 + 7x + 8$?
4. What does $f(x + h) - f(x)$ represent in calculus?
5. How can you find the roots of $f(x)$?

Tip: To handle function transformations, try substituting values into the formula step by step, ensuring correct expansion and simplification.