document.write( "Question 174318: The fuel efficiency for a cetain midsize car is given by: E(v0 = -0.0235 v^2 + 2.768v - 53.85, where E(v) is the fuel efficiency in mpg for a car traveling v mph. What speed will yield the maximum fuel efficiency, and what is taht max fuel efficiency? \n" ); document.write( "

Algebra.Com's Answer #129265 by solver91311(24713) $\"\"$ $\"About$

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Your function is a second degree polynomial in $\"v\"$ , meaning that the graph of the function will be a parabola. Since the lead coefficient is less than zero, you have a parabola that is concave down and you know for sure that the vertex of the parabola is a maximum point.\r
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\n" ); document.write( "\n" ); document.write( "For any parabola expressed in the form $\"f%28x%29=ax%5E2%2Bbx%2Bc\"$ , the vertex is located at the point ( $\"-b%2F2a%29\"$ , $\"f%28-b%2F2a%29\"$ ).\r
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\n" ); document.write( "\n" ); document.write( "All you need to do is calculate $\"v%5Bmfe%5D=-b%2F2a=-2.768%2F%282%2A%28-0.0235%29%29\"$ to determine the velocity that gives the maximum fuel efficiency and then evaluate the function for $\"f%28v%5Bmfe%5D%29\"$ to determine the fuel efficiency at that velocity. \n" ); document.write( "

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