Math Problem Statement

f(3)=2x²-3x+1 table and graph

Solution

Let's break down the problem step by step and address both the table and graph for the quadratic function f(x)=2x23x+1f(x) = 2x^2 - 3x + 1.

1. Table of Values

We can compute the values of f(x)f(x) for different values of xx.

xxf(x)=2x23x+1f(x) = 2x^2 - 3x + 1
-22(2)23(2)+1=8+6+1=152(-2)^2 - 3(-2) + 1 = 8 + 6 + 1 = 15
-12(1)23(1)+1=2+3+1=62(-1)^2 - 3(-1) + 1 = 2 + 3 + 1 = 6
02(0)23(0)+1=12(0)^2 - 3(0) + 1 = 1
12(1)23(1)+1=23+1=02(1)^2 - 3(1) + 1 = 2 - 3 + 1 = 0
22(2)23(2)+1=86+1=32(2)^2 - 3(2) + 1 = 8 - 6 + 1 = 3
32(3)23(3)+1=189+1=102(3)^2 - 3(3) + 1 = 18 - 9 + 1 = 10

2. Graph of f(x)=2x23x+1f(x) = 2x^2 - 3x + 1

To plot this quadratic equation, we can use the points from the table:

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

This should form a parabola opening upwards because the coefficient of x2x^2 is positive.

Let me generate the graph for you.

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Math Problem Analysis

Mathematical Concepts

Algebra
Quadratic Equations
Graphing

Formulas

Quadratic equation formula f(x) = ax² + bx + c

Theorems

Properties of parabolas

Suitable Grade Level

Grades 8-10