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
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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)