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

Question

Responses

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

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

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

(8,14)

Answer 1

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

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

2. Complete the square for the \( x^2 - 16x \) part. To do this, take \( -16 \), divide by 2 to get \( -8 \), and then square it to get \( 64 \). We then add and subtract \( 64 \): \[ y = (x^2 - 16x + 64 - 64) + 14 \]

3. Rewrite the equation: \[ y = (x - 8)^2 - 64 + 14 \]

4. Combine the constants: \[ y = (x - 8)^2 - 50 \]

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

• \( h = 8 \)
• \( k = -50 \)

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

Therefore, the correct response is: (8, -50).