# What is the vertex form of #6y=-x^2 + 9x# ?

##### 1 Answer

Aug 29, 2016

#### Explanation:

Divide both sides by

#y = -1/6(x^2-9x)#

#=-1/6((x-9/2)^2-9^2/2^2)#

#=-1/6(x-9/2)^2+1/6*81/4#

#=-1/6(x-9/2)^2+27/8#

Taking the two ends together, we have:

#y = -1/6(x-9/2)^2+27/8#

which is in vertex form:

#y = a(x-h)^2+k#

with multiplier

graph{(6y+x^2-9x)((x-9/2)^2+(y-27/8)^2-0.02) = 0 [-5.63, 14.37, -3.76, 6.24]}