Given f(x) = x2 + 7x + 8, find the following.
(a)
f(0)
(b)
f(1)
(c)
f(−1)
(d)
f(−3)
(e)
f(a)

(f)
f(x + h)

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.

Given f(x) = x^2 + 7x + 8, find the following. (a) f(0) (b) f(1) (c) f(−1) (d) f(−3) (e) f(a) (f) f(x + h)

Explore how to evaluate and expand the quadratic function f(x) = x^2 + 7x + 8 with specific values such as f(0), f(1), f(-1), f(-3), f(a), and f(x + h). This problem covers core algebraic concepts, including function evaluation and expansion, suitable for Grades 9-11 students.

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