The general vertex form for a parabola with vertex at (a,b) is
color(white)("XXX")color(magenta)y=color(green)m(color(cyan)x-color(red)a)^2+color(blue)b
For the vertex (color(red)a,color(blue)b)=(color(red)(-5),color(blue)4) this becomes
color(white)("XXX")color(magenta)y=color(green)m(color(cyan)x-color(red)((-5)))^2+color(blue)4
color(white)("XXXX") =color(green)m(x+5)^2+color(blue)4
Since this equation hold for the point (color(cyan)x,color(magenta)y)=(color(cyan)6,color(magenta)125)
color(white)("XXX")color(magenta)(125)=color(green)m(color(cyan)6+5)^2+color(blue)(4
color(white)("XXXXX")=color(green)m * 11^2 +color(blue)4
color(white)("XXXXX")=121color(green)m +color(blue)4
rarrcolor(white)("X")121=121color(green)m
rarrcolor(white)("X")color(green)m=1
and the equation is
color(white)("XXX")color(magenta)y=color(green)1(color(cyan)x+5)^2+4
