Evaluate the function f(x) = 2x² - 3x + 1 for x = 3.


To evaluate the function \( f(x) = 2x^2 - 3x + 1 \) for \( x = 3 \), follow these steps:

1. Substitute \( x = 3 \) into the function:
   \[
   f(3) = 2(3)^2 - 3(3) + 1
   \]

2. Calculate \( 3^2 \):
   \[
   3^2 = 9
   \]

3. Multiply by 2:
   \[
   2 \times 9 = 18
   \]

4. Multiply \( -3 \) by 3:
   \[
   -3 \times 3 = -9
   \]

5. Add the results:
   \[
   f(3) = 18 - 9 + 1 = 10
   \]

So, \( f(3) = 10 \).

Would you like more details or have any questions? 

Here are some related questions:

1. What is the value of \( f(x) = 2x^2 - 3x + 1 \) when \( x = -1 \)?
2. How does the graph of \( f(x) = 2x^2 - 3x + 1 \) look?
3. What is the vertex of the function \( f(x) = 2x^2 - 3x + 1 \)?
4. For what values of \( x \) does \( f(x) = 0 \)?
5. How does changing the coefficient of \( x^2 \) in the function affect its graph?

**Tip:** When evaluating functions, substitute the given value of \( x \) carefully, and follow the order of operations: parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right).

Learn how to evaluate the quadratic function f(x) = 2x^2 - 3x + 1 for x = 3 with detailed step-by-step calculations. This problem demonstrates the application of quadratic functions and is suitable for students in Grades 7-9.

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