# How do you write the quadratic in vertex form given y= -3x^2 + 21x?

$y = - 3 {\left(x - \frac{7}{2}\right)}^{2} + \frac{147}{4} = - 3 {\left(x - 3.5\right)}^{2} + 36.75$
$y = - 3 {x}^{2} + 21 x = - 3 \left({x}^{2} - 7 x\right)$
$= - 3 \left({\left(x - \left(\frac{7}{2}\right)\right)}^{2} - {\left(\frac{7}{2}\right)}^{2}\right)$
$= - 3 {\left(x - \left(\frac{7}{2}\right)\right)}^{2} + 3 {\left(\frac{7}{2}\right)}^{2}$
$= - 3 {\left(x - \frac{7}{2}\right)}^{2} + \frac{147}{4}$
$= - 3 {\left(x - 3.5\right)}^{2} + 36.75$
The vertex of the parabola is $\left(3.5 , 36.75\right)$