The general vertex form for a quadratic with vertex at #(color(red)a,color(blue)b)# is
#color(white)("XXX")y=color(green)m(x-color(red)a)^2+color(blue)b#
(where #color(green)m# can be thought of as a "spread" factor).
Given the vertex #(color(red)(-2),color(blue)1)#
this becomes
#color(white)("XXX")y=color(green)m(x-(color(red)(-2)))^2+color(blue)1=color(green)m(x+2)^2+1#
If #(x,y)=(1,8)# is a solution to this equation,
then
#color(white)("XXX")8=color(green)m(1+2)^2+1#
#color(white)("XXX")rarr 7=color(green)mxx9#
#color(white)("XXX")rarr color(green)m=color(green)(7/9)#
and the complete quadratic is
#color(white)("XXX")y=color(green)(7/9)(x+2)^2+1#
