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

Question

• (8,78)
• (8,30)
• (8,14)
• (8,-50)

Answer 1

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

Given equation: y = x^2 - 16x + 14

First, we take the coefficient of x and divide it by 2, and then square the result:
(-16/2)^2 = 64.

Now, we add and subtract this value inside the parentheses to complete the square:
y = (x^2 - 16x + 64 - 64) + 14
= (x^2 - 16x + 64) - 64 + 14
= (x - 8)^2 - 50

So, the vertex of the parabola is (h,k) = (8,-50).

Therefore, the correct answer is: (8,-50)