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

Question

Responses

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

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

(8,30)
left parenthesis 8 comma 30 right parenthesis

(8,14)

Answer 1

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

1. Identify the coefficient of \( x \): The coefficient of \( x \) is -16.

2. Take half of the coefficient and square it: \[ \left(-\frac{16}{2}\right)^2 = (-8)^2 = 64 \]

3. Rewrite the equation: Add and subtract this square inside the equation: \[ y = (x^2 - 16x + 64) - 64 + 14 \] \[ y = (x - 8)^2 - 50 \]

4. Determine the vertex: The vertex form of a parabola is \( y = a(x-h)^2 + k \), where \( (h, k) \) is the vertex. From our equation, we find:

   • \( h = 8 \)
   • \( k = -50 \)

Thus, the vertex is \( (8, -50) \).

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