Complete the square to identify the vertex of y=x^2−16x+14 .(1 point)

Question

Responses

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

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

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

(8,78)

Answer 1

To find the vertex of the quadratic equation \( y = x^2 - 16x + 14 \) by completing the square, follow these steps:

1. Start with the quadratic equation:
   \( y = x^2 - 16x + 14 \).

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

3. Rewrite the equation by adding and subtracting this square inside the equation:
   \( y = (x^2 - 16x + 64) - 64 + 14 \).

4. Simplify the expression:
   \( y = (x - 8)^2 - 50 \).

5. Now, the equation is in the vertex form \( y = a(x - h)^2 + k \), where \( (h, k) \) is the vertex:
   Thus, the vertex \( (h, k) \) is \( (8, -50) \).

Therefore, the vertex of the parabola is:
(8, −50).