document.write( "Question 1198745: Find the quadratic function y = a (x-h)^2 whose graph passes through the given points. (12, -1) and (9, 0) \n" ); document.write( "

Algebra.Com's Answer #832373 by ikleyn(52786) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "Find the quadratic function y = a (x-h)^2 whose graph passes through the given points.
\n" ); document.write( "(12, -1) and (9, 0)
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "First use the info, which goes with the point (9,0).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "It gives you this equation  0 = a*(9-h)^2,\r\n" );
document.write( "\r\n" );
document.write( "from which you conclude that h = 9.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Now use the info, which goes with the point (12,-1).\r\n" );
document.write( "\r\n" );
document.write( "It gives you this equation  -1 = a*(12-9)^2,  or  -1 = a*9,  a = .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Thus the quadratic function is  y = .    ANSWER\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved step by step, with explanations.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "////////////////\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The reasons by @greenestamps are incorrect.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The given form parabola is not a general form parabola, where three points are needed to define it by an unique way.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "It is VERY SPECIAL form of parabolas that touch x-axis.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "For this special form, two given points are just ENOUGH to determine the parabola by an unique way, \r
\n" ); document.write( "\n" ); document.write( "as I did it in my solution.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Of the three parabolas in the plot by @greenestamps, only one touches x-axis.\r
\n" ); document.write( "\n" ); document.write( "It is the parabola shown in red, and only this parabola has the assigned form.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "My solution is correct.\r
\n" ); document.write( "\n" ); document.write( "@greenestamps reasons and solution is not correct.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The problem is not deficient, as @greenestamps states.\r
\n" ); document.write( "\n" ); document.write( "It is posed correctly and has a unique solution, which I found in my post.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "        For your better understanding, the general form parabola has three parameters,\r
\n" ); document.write( "\n" ); document.write( "        and, therefore, requires three points to be determined by a unique way.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "        Parabola, assigned in the post, just has a vertex on x-axis and, therefore, \r
\n" ); document.write( "\n" ); document.write( "        depends on two parameters, \"a\" and \"h\", ONLY.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "        It is why having two points is ENOUGH to determine this parabola by a unique way.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );