The equation of a parabola is y=x2+4x+4. Write the equation in vertex form.

Question

Write any numbers as integers or simplified proper or improper fractions.

Answer 1

To write the equation in vertex form, we need to complete the square.

Starting with y = x^2 + 4x + 4, we first factor out the coefficient of x^2 from the x terms:

y = 1*(x^2 + 4x) + 4

Next, we take half of the coefficient of x (4), square it, and add it inside the parentheses:

y = 1*(x^2 + 4x + 4) - 4 + 4

Then simplify:

y = 1*(x + 2)^2 + 0

So, the equation in vertex form is y = (x + 2)^2.