Complete the square to identify the vertex of y = x^2 - 16x + 14.

Question

A. (8, 30)
B. (8, 14)
C. (8, 78)
D. (8, -50)

Answer 1

To complete the square, we want to rewrite the equation in the form y = a(x - h)^2 + k, where (h, k) is the vertex.

To do this, let's focus on the x^2 and x terms. We can rewrite x^2 - 16x as (x - 8)^2 - 64. (This is found by taking half of the coefficient of the x-term, squaring it, and then subtracting that result.)

We can then substitute this into our original equation to get:
y = (x - 8)^2 - 64 + 14
Simplifying, we get:
y = (x - 8)^2 - 50

Now we can see that the vertex is (8, -50).

So the answer is D. (8, -50)