Let's break down the problem step by step and address both the table and graph for the quadratic function \( f(x) = 2x^2 - 3x + 1 \).

### 1. **Table of Values**
We can compute the values of \( f(x) \) for different values of \( x \).

| \( x \) | \( f(x) = 2x^2 - 3x + 1 \) |
|--------|-----------------------------|
|  -2    | \( 2(-2)^2 - 3(-2) + 1 = 8 + 6 + 1 = 15 \) |
|  -1    | \( 2(-1)^2 - 3(-1) + 1 = 2 + 3 + 1 = 6 \) |
|   0    | \( 2(0)^2 - 3(0) + 1 = 1 \) |
|   1    | \( 2(1)^2 - 3(1) + 1 = 2 - 3 + 1 = 0 \) |
|   2    | \( 2(2)^2 - 3(2) + 1 = 8 - 6 + 1 = 3 \) |
|   3    | \( 2(3)^2 - 3(3) + 1 = 18 - 9 + 1 = 10 \) |

### 2. **Graph of \( f(x) = 2x^2 - 3x + 1 \)**
To plot this quadratic equation, we can use the points from the table:

- For \( x = -2 \), \( f(x) = 15 \)
- For \( x = -1 \), \( f(x) = 6 \)
- For \( x = 0 \), \( f(x) = 1 \)
- For \( x = 1 \), \( f(x) = 0 \)
- For \( x = 2 \), \( f(x) = 3 \)
- For \( x = 3 \), \( f(x) = 10 \)

This should form a parabola opening upwards because the coefficient of \( x^2 \) is positive.

Let me generate the graph for you.

Explore how to generate a table of values and graph the quadratic equation f(x) = 2x² - 3x + 1. This guide covers key algebraic concepts, including quadratic equations, and helps visualize the parabola for different values of x. Ideal for students in Grades 8-10.

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