Write the equation in vertex form

Question

y=x^2+2x+5

Answer 1

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

Starting with the expression x^2 + 2x, we can find the constant term that needs to be added and then subtracted to complete the square.

The constant term that needs to be added is (2/2)^2 = 1.

Adding and subtracting 1 to the expression:
y = x^2 + 2x + 1 - 1 + 5

Next, we can group the trinomial and simplify the equation:
y = (x^2 + 2x + 1) - 1 + 5
y = (x + 1)^2 + 4

Therefore, the equation in vertex form is y = (x + 1)^2 + 4.