Determine the Vertex for the Parabola in Equation: y = (x-7)² - 7

To solve this problem, we need to find the vertex of the given parabola $y = (x-7)^2 - 7$. This equation is already in the vertex form of a parabola, $y = a(x-h)^2 + k$. In this form, the vertex is given by the point $(h, k)$.

Let's break it down:

• The expression inside the parentheses, $(x-7)$, shows that $h = 7$.
• The constant term outside, which is $-7$, shows that $k = -7$.

Therefore, the vertex of the parabola is given by the coordinates $(h, k)$.
Substituting $h = 7$ and $k = -7$ into the vertex form, we have:

Vertex: $(7, -7)$

Therefore, the correct answer is choice 1: $(7, -7)$.