in algebra Rewrite the equation in vertex form. Please show your work y = x² + 4x + 16

Answer 1

To rewrite the equation y = x² + 4x + 16 in vertex form, we need to complete the square.

Step 1: Group the x² and x terms together.
y = (x² + 4x) + 16

Step 2: Take half of the coefficient of x and square it. Add this value inside the parentheses and subtract it outside the parentheses.
y = (x² + 4x + 4) + 16 - 4

Step 3: Factor the quadratic trinomial inside the parentheses.
y = (x + 2)² + 16 - 4

Step 4: Simplify.
y = (x + 2)² + 12

The equation y = x² + 4x + 16 in vertex form is y = (x + 2)² + 12.