document.write( "Question 1199412: find the equation of a parabola with vertex on the line y=2x, axis parallel to the y axis and passing through (3/2, 1) & (3,4) \n" ); document.write( "

Algebra.Com's Answer #833284 by ikleyn(52788) $\"\"$ $\"About$

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\n" ); document.write( "find the equation of a parabola with vertex on the line y=2x,
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document.write( "Looking at the given points, I see that when we are moving from point (3/2,1) to point (3,4),\r\n" );
document.write( "then x-coordinate doubles, while y-coordinate quadruples.\r\n" );
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document.write( "      It leads me to the thought / (to the hypothesis) that the vertex is the point (0,0).\r\n" );
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document.write( "Indeed, then the parabola is  y =  = ,\r\n" );
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document.write( "and all the conditions of the problem are satisfied: the vertex lies on the line y = 2x \r\n" );
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document.write( "at (x,y) = (0,0), and the points do belong to this parabola, as you can easily check\r\n" );
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document.write( "by substituting the coordinates into the equation.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "Notice that my solution is logically irreproachable.\r
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\n" ); document.write( "\n" ); document.write( "        An observation leads me to a hypothesis,\r
\n" ); document.write( "\n" ); document.write( "        and then I check the hypothesis by direct calculations,\r
\n" ); document.write( "\n" ); document.write( "        confirming that all the conditions of the problem are satisfied.\r
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