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To find the function values \( f(x) \) for \( x = 1 \) and \( x = 3 \), we will substitute these values into the given quadratic function:

\[
f(x) = -3x^2 + 12x - 10.
\]

### Step 1: Calculate \( f(1) \)
\[
f(1) = -3(1)^2 + 12(1) - 10.
\]
\[
f(1) = -3 + 12 - 10 = -1.
\]

### Step 2: Calculate \( f(3) \)
\[
f(3) = -3(3)^2 + 12(3) - 10.
\]
\[
f(3) = -27 + 36 - 10 = -1.
\]

Now, we can complete the table:

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

Would you like a detailed explanation of these calculations or have any other questions?

Here are 5 related questions for further exploration:
1. How do you find the axis of symmetry for a quadratic function?
2. What does the vertex of a parabola represent in a real-world context?
3. How can you determine whether a parabola opens upwards or downwards?
4. What is the significance of the discriminant in a quadratic equation?
5. How do you find the roots of a quadratic function using the quadratic formula?

**Tip:** The vertex form of a quadratic function is useful for graphing because it clearly shows the vertex and the direction of the parabola.

Find the vertex of the function f(x) = -3x^2 + 12x - 10 and complete a table with values of f(x) for x = 1, 2, and 3.

Learn how to find the vertex and complete a table of values for the quadratic function f(x) = -3x^2 + 12x - 10. This problem involves key concepts like the vertex of a parabola and using the vertex formula. Suitable for students in Grades 9-11.

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