Question 882959
Convert to vertex form by completing the square.
{{{f(x)=x^2+6x-1}}}
{{{f(x)=x^2+6x+9-1-9}}}
{{{f(x)=(x+3)^2-10}}}
The minimum value occurs at the vertex ({{{-3}}},{{{-10}}}).
For {{{x<-3}}}, {{{f(x)}}} is decreasing.
For {{{x>-3}}}, {{{f(x)}}} is increasing.
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{{{drawing(300,300,-10,10,-15,5,circle(-3,-10,0.32),blue(line(-3,-20,-3,20)),graph(300,300,-10,10,-15,5,x^2+6x-1))}}}