What is the vertex form of #y=-x^2-5x-19#?

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Answer 1 · 2018-04-04T22:44:36

#y=-(x+5/2)^2-51/4#

#y=-x^2-5x-19#

Factor out a -1.

#y=color(red)(-)(x^2color(red)+5xcolor(red)+19)#

Add and subtract #(5/2)^2# within the grouping.

#y=-(x^2+5xcolor(red)(+25/4)+19color(red)(-25/4))#

Factor the first 3 terms of the right hand side.

#y=-[color(red)((x+5/2)^2)+19-25/4]#

Simplify.

#y=-[(x+5/2)^2+color(red)(51/4)]#

#y=color(red)-(x+5/2)^2color(red)-51/4#

graph{-x^2-5x-19 [-5, 1, -20, -10]}