Locate the Vertex of the Parabola: y = (x-6)² + 1

To find the vertex of the parabola given by the equation $y = (x-6)^2 + 1$, we recognize that the equation is in vertex form $y = (x-h)^2 + k$, where $(h, k)$ represents the vertex.

• Step 1: Recognize that the standard vertex form of a parabola is $y = (x-h)^2 + k$.
• Step 2: Identify $h$ and $k$ directly from the equation.
• Step 3: Compare the given equation $y = (x-6)^2 + 1$ to the standard form to determine the values of $h$ and $k$.

From the equation $y = (x-6)^2 + 1$, we identify:

• $h = 6$ (the value that follows the minus sign in $(x-6)$)
• $k = 1$ (the constant term added outside the squared term)

The vertex of the parabola is therefore $(h, k) = (6, 1)$.

Thus, the vertex of the parabola is $(6, 1)$.