Complete the table.



*f*(*x*) = –3*x*2 + 3*x*

*x*

*f*(*x*)

0

1

2

3

Let's complete the table for the given function \( f(x) = -3x^2 + 3x \). We'll evaluate \( f(x) \) for each of the values of \( x \) provided in the table.

### Step-by-step calculation:

1. **For \( x = 0 \):**
   \[
   f(0) = -3(0)^2 + 3(0) = 0
   \]
   So, \( f(0) = 0 \).

2. **For \( x = 1 \):**
   \[
   f(1) = -3(1)^2 + 3(1) = -3(1) + 3 = 0
   \]
   So, \( f(1) = 0 \).

3. **For \( x = 2 \):**
   \[
   f(2) = -3(2)^2 + 3(2) = -3(4) + 6 = -12 + 6 = -6
   \]
   So, \( f(2) = -6 \).

4. **For \( x = 3 \):**
   \[
   f(3) = -3(3)^2 + 3(3) = -3(9) + 9 = -27 + 9 = -18
   \]
   So, \( f(3) = -18 \).

### The completed table is:

\[
\begin{array}{|c|c|}
\hline
x & f(x) \\
\hline
0 & 0 \\
1 & 0 \\
2 & -6 \\
3 & -18 \\
\hline
\end{array}
\]

Would you like further details or have any questions?

Here are 5 related questions to expand your understanding:
1. What is the vertex of the quadratic function \( f(x) = -3x^2 + 3x \)?
2. How do you find the axis of symmetry for this function?
3. What is the range of \( f(x) = -3x^2 + 3x \)?
4. Can you determine where \( f(x) \) is increasing and decreasing?
5. How would the graph of \( f(x) = -3x^2 + 3x \) look like?

**Tip:** The coefficient of \( x^2 \) determines whether a parabola opens upwards or downwards. Here, \( -3 \) makes it open downward!

Complete the table.

f(x) = -3x^2 + 3x

x   |  f(x)
----|------
 0  |
 1  |
 2  |
 3  |

Complete the table for the quadratic function f(x) = -3x^2 + 3x by evaluating the function at different values of x (0, 1, 2, 3). This problem focuses on understanding quadratic functions and applying basic algebraic concepts. Suitable for Grade 9-10 students.

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