Question 408215
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Hi
Write the given expression in the standard vertex form f(x)=a(x-h)^2+k
where(h,k) is the vertex
f(x)=1/3x^2+x+1  |completing the square to put into vertex form
f(x)=1/3[x^2+3x)+1  
f(x)=1/3[x +3/2)^2 -9/4]+1 
f(x)=1/3(x +3/2)^2 -3/4 + 1 
f(x)=1/3(x +3/2)^2 + 1/4   |vertex is Pt(-3/2,1/4) 

{{{drawing(300,300, -6, 6, -6, 6, grid(1),
circle(-1.5, .25,0.3),
circle(0, 1,0.3),
graph( 300, 300, -6, 6, -6, 6,(1/3)x^2+x+1  ))}}}