Complete the square to put equation \(y = x^{2} + 6x + 2\) to the form \(a ( x + h )^{2} + k\)
\(x^{2} + 6x = -2\)
(half the 6 then square it to find the third term and make the LHS into a
perfect square. add the number to both sides \(( \frac{6}{2} )^{2}\))
\(x^{2} + 6x + 9 = -2 + 9\)
(factorise the LHS and simplify the RHS)
\(( x + 3 )^{2} = 7\)
\(( x + 3 )^{2} - 7 = 0\)
In this form, we know that the vertex is (-h , k )
∴ the vertex of this equation is (-(3) , -7 )
