**Write ***y*** = –3***x*** **^{2}** + 24x – 27 in vertex form.**

Move *c* to the other side of the equation.

\(y = −3x^{2} + 24x\ –\ 27\)

\(y\ +\ 27 = −3x^{2} + 24x\)

\(Divide\ by\ a = −3\)

\(−\frac{y}{3}\ −\ 9 = x^{2}\ − 8x\)

Take half of the new *b*, square it, and add that quantity to both sides:

\(\frac{1}{2}(−8) = −4\ and\ (−4)^{2} = 16\)

\(−\frac{y}{3}\ −\ 9\ +\ 16 = x^{2}\ −\ 8x\ +\ 16\)

Write the right side as a squared binomial and simplify.

\(−\frac{y}{3}\ +\ 7\ = (x\ −\ 4)^{2}\)

Rewrite the equation in vertex form.

\(y = −3(x\ −\ 4)^{2}\ 21\)