Evaluate Quadratic Function f(x) = -3x^2 + 3x and Complete the Table

Math Problem Statement

Complete the table.

f(x) = –3x2 + 3x

f(x)

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.

For $x = 0$ : $f(0) = -3(0)^2 + 3(0) = 0$ So, $f(0) = 0$ .
For $x = 1$ : $f(1) = -3(1)^2 + 3(1) = -3(1) + 3 = 0$ So, $f(1) = 0$ .
For $x = 2$ : $f(2) = -3(2)^2 + 3(2) = -3(4) + 6 = -12 + 6 = -6$ So, $f(2) = -6$ .
For $x = 3$ : $f(3) = -3(3)^2 + 3(3) = -3(9) + 9 = -27 + 9 = -18$ So, $f(3) = -18$ .

\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!

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Algebra
Quadratic Functions
Evaluation of Functions

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

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Vertex and Axis of Symmetry Theorem

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