Write y = x2 + 6x + 10 in vertex form

Set the binomial equal to 0, then set aside the constant value 10 and replace it with c.

Find a value for c that completes the square. 0 = x2 + 6x + c

Since x is on the right side of the equation, switch the sides so it is on the left side of the equation. x^2 + 6x = 0

To create a trinomial square on the left side of the equation, find a value that is equal to the square of half of b, the coefficient of x. (b/2) ^ 2 = (3) ^ 2

Add the term to each side of the equation. x^ + 6x + (3) 2 = 0 + (-3) 2

Simplify the equation.

x^2 + 6 x + 9 = 9

Factor the perfect trinomial square into (x + 3) ^ 2. (x + 3) ^ 2 = 9

Move the new constant to the left side of the equation. (x + 3) ^ 2 + (9) = 0

Add the original constant to the new constant. (x + 3) ^ 2 + (9) + (10) = 0

Complete the square in the expression x^2 + 6 x + 10. (x + 3) ^ 2 + 1

Reorder the right side of the equation to match the vertex form of a parabola. y = (x + 3) ^ 2 + 1