complete the square identity the vertex of y = x^2 - 16x + 14
To complete the square for the given quadratic equation y = x^2 - 16x + 14, we need to rewrite it in the form of (x - h)^2 + k, where (h, k) represents the vertex of the parabola.
First, let's group the terms containing x together:
y = (x^2 - 16x) + 14
Next, take half of the coefficient of x (-16) and square it to add and subtract it inside the parentheses:
y = (x^2 - 16x + 64 - 64) + 14
Now, let's rearrange the terms:
y = ((x^2 - 16x + 64) - 64) + 14
The expression inside the parentheses can be rewritten as a perfect square:
y = (x - 8)^2 - 50 + 14
Finally, simplify:
y = (x - 8)^2 - 36
Therefore, the vertex of the parabola is (8, -36).