Complete the square to put equation [tex]y = x^{2} + 6x + 2[/tex] to the form [tex]a ( x + h )^{2} + k [/tex]
[tex] x^{2} + 6x = -2[/tex]
(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 [tex]( \frac{6}{2} )^{2} [/tex])
[tex] x^{2} + 6x + 9 = -2 + 9[/tex]
(factorise the LHS and simplify the RHS)
[tex]( x + 3 )^{2} = 7 [/tex]
[tex]( x + 3 )^{2} - 7 = 0[/tex]
In this form, we know that the vertex is (-h , k )
∴ the vertex of this equation is (-(3) , -7 )
