Complete the square to identify the vertex of y=x2−16x+14 .(1 point) Responses (8,30) left parenthesis 8 comma 30 right parenthesis (8,−50) left parenthesis 8 comma negative 50 right parenthesis (8,78) left parenthesis 8 comma 78 right parenthesis (8,14)

Answer 1

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

1. Group the x terms: \[ y = (x^2 - 16x) + 14 \]

2. Complete the square:

   • We take the coefficient of \( x \) (which is -16), divide it by 2, and square it: \[ \left(\frac{-16}{2}\right)^2 = (-8)^2 = 64 \]
   • Add and subtract this value inside the parentheses: \[ y = (x^2 - 16x + 64 - 64) + 14 \]
   • Now rewrite the equation: \[ y = (x - 8)^2 - 64 + 14 \]

3. Simplify: \[ y = (x - 8)^2 - 50 \]

Now, we can see that the equation of the parabola in vertex form is: \[ y = (x - 8)^2 - 50 \] From this, we can identify the vertex as: \[ (8, -50) \]

Thus, the vertex of the function \( y = x^2 - 16x + 14 \) is \((8, -50)\).

The correct response is: (8, -50).