document.write( "Question 173551: A Parabola with the equation $\"y=ax%5E2\"$ passes through three vertices of a square. if the area of the square = 18, find the value of $\"a\"$ in $\"y=ax%5E2\"$ . \n" ); document.write( "

Algebra.Com's Answer #128436 by Edwin McCravy(20060) $\"\"$ $\"About$

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A Parabola with the equation $\"y=ax%5E2\"$ passes through three vertices of a square. if the area of the square = 18, find the value of $\"a\"$ in $\"y=ax%5E2\"$ .
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document.write( "The formula for the area of a square, where  \r\n" );
document.write( "is the length of each side is \r\n" );
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document.write( "Substitute 18 for A\r\n" );
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document.write( "Take square roots of both sides\r\n" );
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document.write( "So each side is \r\n" );
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document.write( "We draw the square:\r\n" );
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document.write( "Let's draw a diagonal:\r\n" );
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document.write( "Use the Pythagorean theorem to find the length \r\n" );
document.write( "of the diagonal:\r\n" );
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document.write( "Taking square roots:\r\n" );
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document.write( "Now since the diagonal is 6, let's tilt the square\r\n" );
document.write( "45° and put the diagonal along the y-axis with a \r\n" );
document.write( "corner at the origin, like this: \r\n" );
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document.write( "We draw the other diagonal:\r\n" );
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document.write( "Since the vertical diagonal is 6 units,\r\n" );
document.write( "so is the horizontal diagonal, so\r\n" );
document.write( "the two vertices at the end of the\r\n" );
document.write( "horizontal diagonal are \r\n" );
document.write( "and  \r\n" );
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document.write( "We put the coordinates at these corners:\r\n" );
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document.write( "Now we can roughly sketch in the parabola\r\n" );
document.write( "we are looking for:\r\n" );
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document.write( "We put the coordinates at these corners:\r\n" );
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document.write( "Since the parabola has the form ,\r\n" );
document.write( "and goes through , \r\n" );
document.write( "we substitute  and \r\n" );
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document.write( "  \r\n" );
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document.write( "The value of  is therefore  and\r\n" );
document.write( "the equation of the parabola is\r\n" );
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document.write( "  \r\n" );
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document.write( "Edwin

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