Given: #5y = -3x^2 - 2x + 2#

**Vertex form:** #y = a(x-h)^2 + k#,

where the vertex is #(h, k)# and #a# is a constant.

Complete the square to find the vertex form.

First divide by #5# to make #y = #:

#y = (-3/5x^2 - 2/5x )+ 2/5#

Factor out #-3/5# so we only have an #x^2#:

#y = -3/5(x^2 + 2/3 x) + 2/5#

To complete the square we need to multiply #1/2 * 2/3 = 1/3#. We also need to subtract the squared term that we added:

#-3/5 (x+1/3)(x+1/3) = color(red)(-3/5)(x^2 + 2/3x " "color(red)( + 1/9))#

#y = -3/5(x + 1/3)^2 + 2/5 - (color(red)(-3/5 (1/3)^2))#

#y = -3/5(x + 1/3)^2 + 3/3*2/5 + 1/15#

#y = -3/5(x + 1/3)^2 + 7/15#