Question 423658
The formula for the x-variable of the vertex is {{{(-(b/2a))}}}
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f(x) = x2+10x+9 
So identify the a, b, and c coeficients:
a= +1; b = +10; and c=+9
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Plug-in the variables and solve for the x-value:
{{{(-(10/2(1)))}}}
x= -5
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Plug-in x=-5 and solve for the y-variable
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{{{((-5)^2+10(-5)+9)}}}
=25-50+9
y = -16
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so the vertex is (-5, -16)