Question

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)**.