Write y = –3x 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.
\(y = −3(x\ −\ 4)^{2}\ 21\)