Question 198183
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Given: {{{y=4(x+3)^2+1}}}

Expand:
{{{y=4(x^2+6x+9)+1}}}
{{{y=4x^2+24x+36+1}}}
{{{y=4x^2+24x+37}}}, where{{{system(a=4,b=24,c=37)}}}


Solving vertex: (x,y) = (h,k) 


{{{h=-b/2a=-24/(2)(4)=-24/8}}}
{{{red(h=-3=x)}}}


For y: subst. x= -3 to eqn,
{{{y=4(-3)^2+24(-3)+37=4(9)-72+37=36-72+37}}}
{{{red(y=1=h)}}}


Vertex --> (h,k) = (-3,1)


{{{drawing(400,400,-5,5,-5,10,grid(1),graph(400,400,-5,5,-5,10,4(x+3)^2+1), green(circle(-3,1,.10)))}}}


Thank you,
Jojo</font>