To find \( k(a + 3) \) for the given function \( k(x) = -x^2 - 3x + 4 \), we'll substitute \( x = a + 3 \) into the function.

Given:

\[
k(x) = -x^2 - 3x + 4
\]

Substitute \( x = a + 3 \):

\[
k(a + 3) = -(a + 3)^2 - 3(a + 3) + 4
\]

Now, expand and simplify:

1. Expand \( (a + 3)^2 \):
   \[
   (a + 3)^2 = a^2 + 6a + 9
   \]

2. Multiply by \(-1\):
   \[
   -(a^2 + 6a + 9) = -a^2 - 6a - 9
   \]

3. Expand and simplify \( -3(a + 3) \):
   \[
   -3(a + 3) = -3a - 9
   \]

4. Add the constant term \( +4 \):

So,

\[
k(a + 3) = -a^2 - 6a - 9 - 3a - 9 + 4
\]

Combine like terms:

\[
k(a + 3) = -a^2 - 9a - 14
\]

Thus, the final expression for \( k(a + 3) \) is:

\[
k(a + 3) = -a^2 - 9a - 14
\]

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

Here are 5 related questions to consider:

1. What is the vertex of the function \( k(x) = -x^2 - 3x + 4 \)?
2. How does the value of \( k(a + 3) \) change if \( a = -2 \)?
3. What are the roots of the equation \( k(x) = 0 \)?
4. How does the graph of \( k(x) \) compare to the graph of \( x^2 + 3x - 4 \)?
5. What is the maximum value of \( k(x) \) for real \( x \)?

**Tip:** Always double-check your algebraic expansions and simplifications to ensure accuracy in calculations.

Explore how to evaluate the expression k(a + 3) for the quadratic function k(x) = -x^2 - 3x + 4. This problem involves algebraic concepts like function substitution and simplifying expressions, suitable for students in Grades 9-10.

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