document.write( "Question 715744: The height, y, of a ball tossed into the air can be represented by the equation $\"+y=+-x%5E2%2B10x%2B3+\"$ , where x is the elapsed time. What is the equation of the axis of symmetry of this parabola? \n" ); document.write( "

Algebra.Com's Answer #439571 by KMST(5328) $\"\"$ $\"About$

You can put this solution on YOUR website!
It's $\"highlight%28x=5%29\"$ .
\n" ); document.write( "If a parabola has the equation $\"y=ax%5E2%2Bbx%2Bc\"$
\n" ); document.write( "the equation of its axis of symmetry is $\"x=-b%2F2a\"$
\n" ); document.write( "In your case $\"a=-1\"$ and $\"b=10\"$ , so $\"-b%2F2a=-10%2F2%2F%28-1%29=5\"$
\n" ); document.write( "
\n" ); document.write( "However, you do not need to remember formulas if you realize that you can transform the equation $\"+y=+-x%5E2%2B10x%2B3+\"$ into
\n" ); document.write( " $\"y=-%28x-5%29%5E2%2Bsomething\"$
\n" ); document.write( " $\"-%28x-5%29%5E2=-%28x%5E2-10x%2B25%29=-x%5E2%2B10x-25\"$ so adding $\"28\"$ to both sides of
\n" ); document.write( " $\"-%28x-5%29%5E2=-x%5E2%2B10x-25\"$ we get
\n" ); document.write( " $\"-%28x-5%29%5E2%2B28=-x%5E2%2B10x%2B3\"$
\n" ); document.write( "which tells you that $\"y=-%28x-5%29%5E2%2B28\"$ is another form of the equation of your parabola,
\n" ); document.write( "and this form tells you that the maximum height is 28, reached at time 5. \n" ); document.write( "

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