Complete the square to identify the vertex of y = x^2 – 16x + 14.

Answer 1

To complete the square and identify the vertex of the equation y = x^2 - 16x + 14, we first need to take half of the coefficient of x and square it.

Half of -16 is -8, and (-8)^2 is 64.

To complete the square, we add 64 to both sides of the equation:

y + 64 = x^2 - 16x + 14 + 64

Simplifying the right side:

y + 64 = x^2 - 16x + 78

Next, we can rewrite the right side as a perfect square trinomial by factoring the quadratic expression:

y + 64 = (x - 8)^2 + 78 - 64

Simplifying further:

y + 64 = (x - 8)^2 + 14

Finally, we subtract 64 from both sides to isolate y:

y + 64 - 64 = (x - 8)^2 + 14 - 64

y = (x - 8)^2 - 50

The completed square form of the equation is y = (x - 8)^2 - 50.

From this form, we can identify that the vertex of the parabola is at (8, -50).