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

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

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

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

Answer 1

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

1. Start with the equation: \[ y = x^2 - 16x + 14 \]

2. Rearrange the equation to focus on the \( x \) terms: \[ y = (x^2 - 16x) + 14 \]

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

4. Add and subtract 64 inside the parentheses: \[ y = (x^2 - 16x + 64 - 64) + 14 \]

5. This can be rewritten as: \[ y = (x - 8)^2 - 64 + 14 \]

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

Now we have the equation in vertex form \( y = (x - 8)^2 - 50 \), where the vertex is at \( (h, k) = (8, -50) \).

Thus, the vertex of the function is: \[ \boxed{(8, -50)} \]