Questions: Consider the following function. g(x)=(x-5)^2-4 Step 2 of 4 : Find the x-intercepts, if any. Express the intercept(s) as ordered pair(s).

Solution Steps

To find the \(x\)-intercepts of the function \(g(x) = (x-5)^2 - 4\), we need to determine the values of \(x\) for which \(g(x) = 0\). This involves solving the equation \((x-5)^2 - 4 = 0\). Once we find the solutions for \(x\), we can express the intercepts as ordered pairs \((x, 0)\).

To find the \(x\)-intercepts of the function \(g(x) = (x-5)^2 - 4\), we set the equation equal to zero: \[ (x-5)^2 - 4 = 0 \]

We can rearrange the equation: \[ (x-5)^2 = 4 \] Taking the square root of both sides gives us: \[ x - 5 = \pm 2 \] This results in two equations:

1. \(x - 5 = 2\)
2. \(x - 5 = -2\)

Solving these equations, we find:

1. \(x = 7\)
2. \(x = 3\)

The \(x\)-intercepts can be expressed as ordered pairs: \[ (3, 0) \quad \text{and} \quad (7, 0) \]

Final Answer