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Given the function [tex]f(x) = 7x^2 - 6x + 1[/tex], calculate the following values:

[tex]f(-2) = \ \square[/tex]

[tex]f(-1) = \ \square[/tex]

[tex]f(0) = \ \square[/tex]

[tex]f(1) = \ \square[/tex]

[tex]f(2) = \ \square[/tex]

Sagot :

GinnyAnswer
Alright, let's evaluate the given function [tex]\( f(x) = 7x^2 - 6x + 1 \)[/tex] at different values of [tex]\( x \)[/tex].

1. For [tex]\( x = -2 \)[/tex]:
[tex]\[ f(-2) = 7(-2)^2 - 6(-2) + 1 \][/tex]
[tex]\[ (-2)^2 = 4 \][/tex]
[tex]\[ 7 \cdot 4 = 28 \][/tex]
[tex]\[ -6 \cdot (-2) = 12 \][/tex]
[tex]\[ 28 + 12 + 1 = 41 \][/tex]
So, [tex]\( f(-2) = 41 \)[/tex].

2. For [tex]\( x = -1 \)[/tex]:
[tex]\[ f(-1) = 7(-1)^2 - 6(-1) + 1 \][/tex]
[tex]\[ (-1)^2 = 1 \][/tex]
[tex]\[ 7 \cdot 1 = 7 \][/tex]
[tex]\[ -6 \cdot (-1) = 6 \][/tex]
[tex]\[ 7 + 6 + 1 = 14 \][/tex]
So, [tex]\( f(-1) = 14 \)[/tex].

3. For [tex]\( x = 0 \)[/tex]:
[tex]\[ f(0) = 7(0)^2 - 6(0) + 1 \][/tex]
[tex]\[ 0 = 0 \][/tex]
[tex]\[ 7 \cdot 0 = 0 \][/tex]
[tex]\[ -6 \cdot 0 = 0 \][/tex]
[tex]\[ 0 + 0 + 1 = 1 \][/tex]
So, [tex]\( f(0) = 1 \)[/tex].

4. For [tex]\( x = 1 \)[/tex]:
[tex]\[ f(1) = 7(1)^2 - 6(1) + 1 \][/tex]
[tex]\[ (1)^2 = 1 \][/tex]
[tex]\[ 7 \cdot 1 = 7 \][/tex]
[tex]\[ -6 \cdot 1 = -6 \][/tex]
[tex]\[ 7 - 6 + 1 = 2 \][/tex]
So, [tex]\( f(1) = 2 \)[/tex].

5. For [tex]\( x = 2 \)[/tex]:
[tex]\[ f(2) = 7(2)^2 - 6(2) + 1 \][/tex]
[tex]\[ (2)^2 = 4 \][/tex]
[tex]\[ 7 \cdot 4 = 28 \][/tex]
[tex]\[ -6 \cdot 2 = -12 \][/tex]
[tex]\[ 28 - 12 + 1 = 17 \][/tex]
So, [tex]\( f(2) = 17 \)[/tex].

Thus, the calculated values of the function are:
[tex]\[ f(-2) = 41 \][/tex]
[tex]\[ f(-1) = 14 \][/tex]
[tex]\[ f(0) = 1 \][/tex]
[tex]\[ f(1) = 2 \][/tex]
[tex]\[ f(2) = 17 \][/tex]
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