Question

the graph of the function is a translation of the graph of \\(f(x) = x^2\\). graph the function.

\\g(x) = (x - 5)^2\\

Explanation:

Identify the horizontal translation

$$ g(x) = (x - 5)^2 $$

The graph of \(g(x)\) is a horizontal translation of \(f(x) = x^2\) to the right by \(5\) units.

Determine key points for graphing

$$
LATEXBLOCK0
$$

Plot the parabola

The parabola opens upward with its vertex at \((5, 0)\) and passes through \((3, 4)\), \((7, 4)\), \((1, 16)\), and \((9, 16)\).

Answer:

To graph the function \(g(x) = (x - 5)^2\), plot the parabola with its vertex at \((5, 0)\) and passing through the point \((7, 4)\) (or any other point satisfying the equation, such as \((3, 4)\)).