document.write( "Question 689466: bOB OWN A WATCH REPAIR SHOP. hE HAS found that the cost of operating his shop is given by c(x) = 2x^2-112x+58, where c is cost and x is the number of watches repaired. how many watches must he repari to have the lowest cost? \n" ); document.write( "

Algebra.Com's Answer #425972 by lwsshak3(11628) $\"\"$ $\"About$

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bOB OWN A WATCH REPAIR SHOP. hE HAS found that the cost of operating his shop is given by c(x) = 2x^2-112x+58, where c is cost and x is the number of watches repaired. how many watches must he repair to have the lowest cost?
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\n" ); document.write( "c(x) = 2x^2-112x+58
\n" ); document.write( "This is an equation of a parabola that opens upwards, (curve has a minimum)
\n" ); document.write( "Its standard form: y=A(x-h)^2+k, (h,k)=(x,y) coordinates of the vertex. (y-value is the minimum in this case.
\n" ); document.write( "c(x) = 2x^2-112x+58
\n" ); document.write( "complete the square
\n" ); document.write( "c(x)=2(x^2-56x+28^2)-2*28^2+58
\n" ); document.write( "c(x)=2(x^2-56x+784)-1568+58
\n" ); document.write( "c(x)=2(x-28)^2-1510
\n" ); document.write( "vertex: (28,-1510)
\n" ); document.write( "how many watches must he repair to have the lowest cost? 28
\n" ); document.write( "see graph below as a visual check
\n" ); document.write( " $\"+graph%28+300%2C+300%2C+-50%2C100%2C+-2000%2C+200%2C+2x%5E2-112x%2B58%29+\"$
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