Complete the square to identify the vertex of y=x2−16x+14 .(1 point)

To complete the square for the quadratic equation \( y = x^2 - 16x + 14 \), we can follow these steps:

1. Start with the given equation:
\[
y = x^2 - 16x + 14
\]

2. Move the constant \( 14 \) to the other side, but keep it for reference:
\[
y - 14 = x^2 - 16x
\]

3. To complete the square on the right side, we take half of the coefficient of \( x \), which is \( -16 \), divide it by 2 to get \( -8 \), and then square it to get \( 64 \).

4. Add and subtract \( 64 \) inside the equation:
\[
y - 14 = (x^2 - 16x + 64) - 64
\]
\[
y - 14 = (x - 8)^2 - 64
\]

5. Now, simplify:
\[
y = (x - 8)^2 - 64 + 14
\]
\[
y = (x - 8)^2 - 50
\]

6. The equation is now in vertex form \( y = a(x - h)^2 + k \), where \( (h, k) \) is the vertex. Thus, the vertex is:
\[
(8, -50)
\]

Therefore, the vertex of the parabola is \(\boxed{(8, -50)}\).