Complete the square to identify the vertex of y=x2−16x+14

Question

.(1 point)
Responses

(8,78)
left parenthesis 8 comma 78 right parenthesis

(8,−50)
left parenthesis 8 comma negative 50 right parenthesis

(8,14)
left parenthesis 8 comma 14 right parenthesis

(8,30)

Answer 1

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

1. Take the coefficient of \( x \) (which is -16), divide it by 2 to get -8, and then square it to get 64.

2. Rewrite the equation, adding and subtracting this square:

   \[ y = (x^2 - 16x + 64) - 64 + 14 \]

3. Simplify the equation:

   \[ y = (x - 8)^2 - 64 + 14 \] \[ y = (x - 8)^2 - 50 \]

4. This shows that the vertex form of the equation is \( y = (x - 8)^2 - 50 \).

The vertex of the parabola is at the point \( (8, -50) \).

Therefore, the answer is:

(8, -50)