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The given function is:

\[
f(x) = -x^2 + 6x + 5
\]

You are asked to calculate the values of \( f(x) \) for \( x \) ranging from \( -1 \) to \( 7 \), and fill the table accordingly.

We will substitute each value of \( x \) into the function to get the corresponding \( f(x) \).

### Calculations:

1. **For \( x = -1 \):**
   \[
   f(-1) = -(-1)^2 + 6(-1) + 5 = -1 - 6 + 5 = -2
   \]

2. **For \( x = 0 \):**
   \[
   f(0) = -(0)^2 + 6(0) + 5 = 5
   \]

3. **For \( x = 1 \):**
   \[
   f(1) = -(1)^2 + 6(1) + 5 = -1 + 6 + 5 = 10
   \]

4. **For \( x = 2 \):**
   \[
   f(2) = -(2)^2 + 6(2) + 5 = -4 + 12 + 5 = 13
   \]

5. **For \( x = 3 \):**
   \[
   f(3) = -(3)^2 + 6(3) + 5 = -9 + 18 + 5 = 14
   \]

6. **For \( x = 4 \):**
   \[
   f(4) = -(4)^2 + 6(4) + 5 = -16 + 24 + 5 = 13
   \]

7. **For \( x = 5 \):**
   \[
   f(5) = -(5)^2 + 6(5) + 5 = -25 + 30 + 5 = 10
   \]

8. **For \( x = 6 \):**
   \[
   f(6) = -(6)^2 + 6(6) + 5 = -36 + 36 + 5 = 5
   \]

9. **For \( x = 7 \):**
   \[
   f(7) = -(7)^2 + 6(7) + 5 = -49 + 42 + 5 = -2
   \]

### Completed Table:

\[
\begin{array}{|c|c|c|c|c|c|c|c|c|}
\hline
x & -1 & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\
\hline
f(x) & -2 & 5 & 10 & 13 & 14 & 13 & 10 & 5 & -2 \\
\hline
\end{array}
\]

Let me know if you want further details, and here are five follow-up questions based on this:

1. How can you find the vertex of the quadratic function?
2. What is the domain and range of the function?
3. What is the axis of symmetry for the function \( f(x) \)?
4. How does the sign of the leading coefficient affect the shape of the parabola?
5. What are the roots of the function \( f(x) \)?

**Tip:** When working with quadratic functions, their maximum or minimum value occurs at the vertex.

Soit une fonction f définie par son expression algébrique tel que f(x) = -x^2 + 6x + 5 sur l'intervalle [-1;7], c'est à dire pour des valeurs de x comprises entre -1 et 7. Compléter le tableau de valeurs.

Learn how to complete the table of values for the quadratic function f(x) = -x^2 + 6x + 5, evaluated for x values between -1 and 7. This exercise covers function evaluation, quadratic function properties, and provides a step-by-step approach suitable for students in Grades 9-11.

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