Answered

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Examine the table below:

[tex]\[
\begin{tabular}{|c|c|}
\hline
-8 & 13 \\
\hline
-7 & 6 \\
\hline
-6 & 1 \\
\hline
-5 & -2 \\
\hline
-4 & -3 \\
\hline
-3 & -2 \\
\hline
-2 & 1 \\
\hline
-1 & 6 \\
\hline
0 & 13 \\
\hline
\end{tabular}
\][/tex]

What is the equation of [tex]\( f(x) \)[/tex]?

A. [tex]\( f(x) = (x+5)^2 - 2 \)[/tex]

B. [tex]\( f(x) = (x+4)^2 - 3 \)[/tex]

C. [tex]\( f(x) = (x-4)^2 - 3 \)[/tex]

D. [tex]\( f(x) = (x-5)^2 - 2 \)[/tex]

Sagot :

GinnyAnswer
To determine the correct equation of [tex]\( f(x) \)[/tex], we will compare the given data in the table with each of the provided functions:

1. Function [tex]\( f(x) = (x+5)^2 - 2 \)[/tex]:
- Calculate [tex]\( f(-8) \)[/tex]:
[tex]\[ (-8 + 5)^2 - 2 = (-3)^2 - 2 = 9 - 2 = 7 \][/tex]
This does not match the table value of 13.

2. Function [tex]\( f(x) = (x+4)^2 - 3 \)[/tex]:
- Calculate [tex]\( f(-8) \)[/tex] and compare to other values:
[tex]\[ f(-8) = (-8 + 4)^2 - 3 = (-4)^2 - 3 = 16 - 3 = 13 \][/tex]
[tex]\[ f(-7) = (-7 + 4)^2 - 3 = (-3)^2 - 3 = 9 - 3 = 6 \][/tex]
[tex]\[ f(-6) = (-6 + 4)^2 - 3 = (-2)^2 - 3 = 4 - 3 = 1 \][/tex]
[tex]\[ f(-5) = (-5 + 4)^2 - 3 = (-1)^2 - 3 = 1 - 3 = -2 \][/tex]
[tex]\[ f(-4) = (-4 + 4)^2 - 3 = (0)^2 - 3 = 0 - 3 = -3 \][/tex]
[tex]\[ f(-3) = (-3 + 4)^2 - 3 = (1)^2 - 3 = 1 - 3 = -2 \][/tex]
[tex]\[ f(-2) = (-2 + 4)^2 - 3 = (2)^2 - 3 = 4 - 3 = 1 \][/tex]
[tex]\[ f(-1) = (-1 + 4)^2 - 3 = (3)^2 - 3 = 9 - 3 = 6 \][/tex]
[tex]\[ f(0) = (0 + 4)^2 - 3 = (4)^2 - 3 = 16 - 3 = 13 \][/tex]
All values match the table, indicating a potential solution.

3. Function [tex]\( f(x) = (x-4)^2 - 3 \)[/tex]:
- Calculate [tex]\( f(-8) \)[/tex]:
[tex]\[ (-8 - 4)^2 - 3 = (-12)^2 - 3 = 144 - 3 = 141 \][/tex]
This does not match the table value of 13.

4. Function [tex]\( f(x) = (x-5)^2 - 2 \)[/tex]:
- Calculate [tex]\( f(-8) \)[/tex]:
[tex]\[ (-8 - 5)^2 - 2 = (-13)^2 - 2 = 169 - 2 = 167 \][/tex]
This does not match the table value of 13.

Based on the calculations, the function that fits all the given values in the table is [tex]\( f(x) = (x+4)^2 - 3 \)[/tex].

Thus, the correct equation for [tex]\( f(x) \)[/tex] is:
[tex]\[ f(x) = (x+4)^2 - 3 \][/tex]
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