document.write( "Question 764742: Neglecting air resistance, the height of a projectile fired vertically into the air at an initial velocity of 112 feet per second is a function of time x and is given by the equation f(x) = 112x - 16x2. Find the highest point reached by the projectile. \n" ); document.write( "

Algebra.Com's Answer #465695 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"+f%28x%29+=+112x+-+16x%5E2+\"$
\n" ); document.write( "This is a parabola in the form
\n" ); document.write( " $\"+f%28x%29+=+ax%5E2+%2B+b%2Ax+\"$
\n" ); document.write( "The x-coordinate of the
\n" ); document.write( "vertex ( maximum height )
\n" ); document.write( "is at $\"+-b+%2F+%282a%29+\"$
\n" ); document.write( "----------------
\n" ); document.write( " $\"+a+=+-16+\"$
\n" ); document.write( " $\"+b+=+112+\"$
\n" ); document.write( "------------
\n" ); document.write( " $\"+-b%2F%282a%29+=+-112+%2F+%28+2%2A%28-16%29%29+\"$
\n" ); document.write( " $\"+-b%2F%282a%29+=+3.5+\"$
\n" ); document.write( "Now find $\"+f%283.5%29+\"$
\n" ); document.write( " $\"+f%283.5%29+=+112%2A3.5+-+16%2A3.5%5E2+\"$
\n" ); document.write( " $\"+f%283.5%29+=+392+-+196+\"$
\n" ); document.write( " $\"+f%283.5%29+=+196+\"$
\n" ); document.write( "The highest point is at 196 ft
\n" ); document.write( "Here's the plot:
\n" ); document.write( " $\"+graph%28+400%2C+400%2C+-2%2C+12%2C+-20%2C+220%2C+-16x%5E2+%2B+112x+%29+\"$
\n" ); document.write( "
\n" ); document.write( " \n" ); document.write( "

\n" );