Question 1040585
{{{ F(x) = -.016x^2 + 1.44x + 5.4 }}}
(a)
What is the fuel efficiency if the car’s speed is 20 mph? 
{{{ F(20) = -.016*20^2 + 1.44*20 + 5.4 }}}
{{{ F(20) = -.016*400 + 28.8 + 5.4 }}}
{{{ F(20) = -6.4 + 28.8 + 5.4 }}}
{{{ F(20) = 27.8 }}} mi/gal
Check my math on this!
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This is a parabola, so it has either a single maximum or
a single  minimum.
The minus sign in front of the {{{ x^2 }}} term tells me
this is a maximum
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The formula for the x-value of the vertex ( peak ) is:
{{{ x[v] = -b/(2a) }}} when the form of the equation is:
{{{ y = ax^2 + b*x + c }}}
{{{ a = -.016 }}}
{{{ b = 1.44 }}}
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{{{ x[v] = -1.44 / ( 2*(-.016) ) }}}
{{{ x[v] = 1.44 / .032 }}}
{{{ x[v] = 45 }}}
This says the peak mi/gal occurs when the speed is 45 mi/hr
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Plug this value of {{{ x }}} back into the equation
{{{ F(45) = -.016*45^2 + 1.44*45 + 5.4 }}}
{{{ F(45) = -.016*2025 + 64.8 + 5.4 }}}
{{{ F(45) = -32.4 + 64.8 + 5.4 }}}
{{{ F(45) = 37.8 }}}
The maximum fuel efficiency is 37.8 mi/gal
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Here's the plot:
 {{{ graph( 400, 400, -10, 100, -10, 50, -.016*x^2 + 1.44x + 5.4 ) }}}