document.write( "Question 1097586: how do you know if a parabola opens up or down? \n" ); document.write( "

Algebra.Com's Answer #712033 by KMST(5328) $\"\"$ $\"About$

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A parabola that opens up or down has an equation of the form
\n" ); document.write( " $\"y=a%2Ax%5E2%2Bb%2Ax%2Bc\"$ where $\"a%3C%3E0%29\"$ , $\"b\"$ and $\"c\"$ are real numbers.
\n" ); document.write( "If $\"a%3E0\"$ , as $\"abs%28x%29\"$ increases, $\"ax%5E2%3E0\"$ increases,
\n" ); document.write( "taking the graph up, up and away.
\n" ); document.write( "The terms $\"bx\"$ and $\"c\"$ could be pulling in the opposite direction,
\n" ); document.write( "but as $\"x%5E2\"$ increases faster than $\"abs%28x%29\"$ ,
\n" ); document.write( "eventually the $\"ax%5E2\"$ term will win.
\n" ); document.write( "The graph looks like a smiley face, or like a bowl with the opening pointing up.
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\n" ); document.write( "If $\"a%3C0\"$ , $\"ax%5E2%3C0\"$ and going down as $\"abs%28x%29\"$ increases.
\n" ); document.write( "no matter what the values of $\"b\"$ and $\"c\"$ are,
\n" ); document.write( " $\"y\"$ will eventualy be negative and decreasing,
\n" ); document.write( "so the graph goes down to the left and the right,
\n" ); document.write( "like a frown or an umbrella, and we say it opens down.
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