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The table for values of \( f(x)=x^2 \) and \( g(x)=(x-8)^2 \) is shown below:

[tex]\[
\begin{tabular}{|c|c|c|}
\hline
\multicolumn{2}{|c|}{[tex]$f(x)$[/tex]} & [tex]$g(x)$[/tex] \\
\hline
[tex]$x$[/tex] & [tex]$f(x)$[/tex] & [tex]$g(x)$[/tex] \\
\hline
[tex]$a$[/tex] & [tex]$b$[/tex] & [tex]$c$[/tex] \\
\hline
\end{tabular}
\][/tex]

What are the values of [tex]\( a, b \)[/tex], and [tex]\( c \)[/tex]?



Answer :

GinnyAnswer
Sure, let's find the values of \(a\), \(b\), and \(c\) for the given functions and points.

We start with the function definitions:
- \(f(x) = x^2\)
- \(g(x) = (x - 8)^2\)

Next, we evaluate these functions at the specified points:

1. Evaluate \(f(x)\) at \(x = 2\) to find \(a\):
[tex]\[ f(2) = 2^2 = 4 \][/tex]
So, \(a = 4\).

2. Evaluate \(g(x)\) at \(x = 0\) to find \(b\):
[tex]\[ g(0) = (0 - 8)^2 = (-8)^2 = 64 \][/tex]
So, \(b = 64\).

3. Evaluate \(g(x)\) at \(x = 4\) to find \(c\):
[tex]\[ g(4) = (4 - 8)^2 = (-4)^2 = 16 \][/tex]
So, \(c = 16\).

Therefore, the values are:
- \(a = 4\)
- \(b = 64\)
- [tex]\(c = 16\)[/tex]

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