The
[tex]3x^2 + 24x + 36 = 0 \implies 3(x^2 + 8x) + 36 = 0 \implies \\ \\ 3\left\{x^2 + {\bf 8}x + \left(\frac{\bf 8}{2} \right)^2 - \left(\frac{\bf 8}{2} \right)^2 \right\} + 36 = 0 \implies \\ \\ 3\left\{x^2 + {\bf 8}x + 16 - 16 \right\} + 36 = 0 \implies \\ 3\Big\{(x+4)^2 - 16 \Big\} + 36 = 0 \implies \\ \\ 3(x+4)^2 - 16(3) + 36 = 0 \implies 3(x+4)^2 - 12 = 0 [/tex]
The vertex is (-4, 12) because a(x - b)^2 + c has vertex (b, c) so 3(x+4)^2 - 12 has vetex (-4, 12)
