Find the Vertex of y=(x-5)²+1: Parabola Analysis

To solve this problem, we will determine the vertex of the parabola from the equation $y = (x-5)^2 + 1$, which is in vertex form.

• Step 1: Recognize the form of the quadratic.
  The given equation is $y = (x-5)^2 + 1$, resembling the vertex form $y = a(x-h)^2 + k$.
• Step 2: Identify the vertex parameters $(h, k)$.
  In the equation $y = (x-5)^2 + 1$:
  $h = 5$ and $k = 1$.
• Step 3: Write down the coordinates of the vertex based on the identified values.
  Therefore, the vertex of the parabola is at the point $(5, 1)$.

Thus, the vertex of the parabola is $(5, 1)$.