SOLUTION: I asked this question earlier and I still do not understand how to get to my answer. I double checked for accuracy with typing out the question and this is the correct way... Aki'

Question 468320: I asked this question earlier and I still do not understand how to get to my answer. I double checked for accuracy with typing out the question and this is the correct way...
Aki's Bicycle Designs has determined that when X hundred bicycles are built, the average cost per bicycle is given by C(X)= 0.2x^2-1.9x+8.394, where C(x) is in hundreds of dollars. How many bicycles should the shop build to maximize the average cost per bicycle?
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
I asked this question earlier and I still do not understand how to get to my answer. I double checked for accuracy with typing out the question and this is the correct way...
Aki's Bicycle Designs has determined that when X hundred bicycles are built, the average cost per bicycle is given by C(X)= 0.2x^2-1.9x+8.394, where C(x) is in hundreds of dollars. How many bicycles should the shop build to maximize the average cost per bicycle.
...
I assume you meant minimize the average cost per bicycle instead of maximize.
..
Standard form for a parabola: y=(x-h)^2+k, with (h,k) being the (x,y) coordinates of the vertex.
C(x)=0.2x^2-1.9x+8.394
completing the square
C(x)=.2(x^2-1.9/.2x)+8.394
C(x)=.2(x^2-9.5x+(9.5/2)^2)+8.394-.2(9.5/2)^2
C(x)=.2(x-4.75)^2+8.394-4.513
C(x)=.2(x-4.75)^2+3.881
Vertex:(4.75, 3.881)
Ans:
The shop must build around 475 bicycles to realize the minimum the average cost per bicycle of around $388.
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