Complete the square to identify the vertex of y=x2−16x+14 .(1 point) Responses (8,30) left parenthesis 8 comma 30 right parenthesis (8,78) left parenthesis 8 comma 78 right parenthesis (8,−50) left parenthesis 8 comma negative 50 right parenthesis (8,14) left parenthesis 8 comma 14 right parenthesis

Answer 1

To complete the square for the given quadratic equation y=x^2 - 16x + 14, we need to follow these steps:

Step 1: Take half of the coefficient of x, and square it.
Half of the coefficient of x is -16/2 = -8.
Square of -8 is (-8)^2 = 64.

Step 2: Add the value obtained in Step 1 to both sides of the equation.
y + 64 = x^2 - 16x + 64 + 14
Simplifying, we get:
y + 64 = x^2 - 16x + 78

Step 3: Rewrite the right side of the equation as a perfect square trinomial.
The right side of the equation can be written as:
y + 64 = (x - 8)^2 + 78

Step 4: Subtract 64 from both sides of the equation.
y + 64 - 64 = (x - 8)^2 + 78 - 64
Simplifying, we get:
y = (x - 8)^2 + 14

Comparing the equation in Step 4 to the vertex form of a parabola, y = (x - h)^2 + k,
we can see that the vertex of the given quadratic equation is at the point (h, k) = (8, 14).

Therefore, the correct answer is:
(8, 14)