The standard 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)bcolor(white)("XX")#where #color(green)m# can be thought of as a measure of "spread".
With a vertex of #(color(red)(-2),color(blue)(-3))# this becomes
#color(white)("XXX")y=color(green)m(x-(color(red)(-2)))^2+(color(blue)(-3))#
or
#color(white)("XXX")y=color(green)m(x+2)^2-3#
Given that #(x,y)=(-4,25)# is a solution for the required quadratic we have:
#color(white)("XXX")25=color(green)m((-4)+2)^2-3#
#color(white)("XXX")rarr color(green)m(-2)^2=28#
#color(white)("XXX")rarr color(green)4color(green)m=28#
#color(white)("XXX")rarrrcolor(green)m=7#
and the complete quadratic equation becomes:
#color(white)("XXX")y=7(x+2)^2-3#
