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]
