To write the equation of the parabola \(y = x^2 - 10x + 25\) in vertex form, we need to complete the square. The vertex form of a parabolic equation is \(y = a(x-h)^2 + k\), where \((h, k)\) represents the vertex of the parabola.
1. Rewrite the given equation \(y = x^2 - 10x + 25\) as a completed square trinomial:
\[y = (x^2 - 10x + 25 - 25) + 25\]
\[y = (x^2 - 10x + 25) - 25 + 25\]
\[y = (x - 5)^2 + 0\]
2. Therefore, the equation of the parabola in vertex form is:
\[y = (x - 5)^2\]
In this form, the vertex of the parabola is at the point \((5, 0)\). The vertex form allows us to easily identify the vertex and the direction of the parabola's opening.
