First return this to the form of #y=ax^2+bx+c#
#y=color(blue)((-x-1))color(brown)((x+7))#
Multiply everything in the right hand bracket by everything in the left.
#y=color(brown)(color(blue)(-x)(x+7)color(blue)(" "-1)(x+7))#
#y=-x^2+7x" "-x-7#
#y=-x^2+6x-7.............................Equation(1)#
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Write as: #y=-1(x^2-6x)-7+k#
The #k# corrects the error this process introduces.
Move the power from #x^2# to the outside of the btackets
#y=-1(x-6x)^2-7+k#
Halve the 6 from #6x#
#y=-1(x-3x)^2-7+k#
Remove the #x# from the #3x#
#y=-1(x-3)^2-7+k......................Equation(1_a)#
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Dealing with the error
If you were to expand the brackets and multiply by the -1 you have the value of #(-1)(-3)^2 =-9#. Looking back at #Equation(1)# you will observe that this value is not in it. So we have to remove the #-9#
Set #-9+k=0 => k=9#
.....................................................................................
Substitute for #k" in "Equation(1_a)#
#y=-1(x-3)^2-7+k color(green)(" "->" "y=-1(x-3)^2-7+9)#
#y=-1(x color(magenta)(-3))^2color(blue)(+2) #
#x_("vertex")=(-1)xx color(magenta)((-3)) =+3#
#y_("vertex")=color(blue)(+2)#
#"Vertex"->(x,y)=(3,2)#
