Rewrite the equation in vertex form. Please show your work
y = x^2 + 4x + 16
To rewrite the equation in vertex form, we can complete the square.
Starting with the equation y = x^2 + 4x + 16, let's begin by adding and subtracting the square of half of the coefficient of x from the equation:
y = x^2 + 4x + 4 - 4 + 16
To complete the square, we take the square of half of the coefficient of x and add it to both sides of the equation:
y + 4 = x^2 + 4x + 4 + 12
Next, we rearrange the terms within the parentheses:
y + 4 = (x^2 + 4x + 4) + 12
Now, we factor the perfect square trinomial within the parentheses:
y + 4 = (x + 2)^2 + 12
Therefore, the equation in vertex form becomes:
y = (x + 2)^2 +