document.write( "Question 808522: I have a Graph with the vertex as a 'minimum' and with a turning point of 'x' intercept 5 and -2 and a 'y' intercept of -10. Turning point is -12y & 1.5x.\r
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\n" ); document.write( "I'm very confused with this one can I PLEASE get some help. I wish I could show you the graph as it will make it much easier.\r
\n" ); document.write( "\n" ); document.write( "Thank you! \n" ); document.write( "

Algebra.Com's Answer #487058 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!
have a Graph with the vertex as a 'minimum' and with a turning point of 'x' intercept 5 and -2 and a 'y' intercept of -10. Turning point is -12y & 1.5x.
\n" ); document.write( " I need to find 'equations' that fit this graph and give two reasons for my answer.
\n" ); document.write( " I'm very confused with this one can I PLEASE get some help. I wish I could show you the graph as it will make it much easier.
\n" ); document.write( " Thank you!\r
\n" ); document.write( "\n" ); document.write( "

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document.write( "To have x-intercepts at 5 and -2, it must be such that if you let\r\n" );
document.write( "y=0 and solve for x you get \r\n" );
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document.write( "              x = 5; and  x = -2\r\n" );
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document.write( "That would be gotten be setting\r\n" );
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document.write( "           x-5 = 0; and x+2 = 0\r\n" );
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document.write( "That means you must have had to use the zero factor principle on\r\n" );
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document.write( "              (x-5)(x+2)=0\r\n" );
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document.write( "And there could have been any constant times that\r\n" );
document.write( "and we would have gotten the same two x-intercepts.\r\n" );
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document.write( "So the equation must have been \r\n" );
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document.write( "            y = a(x-5)(x+2) \r\n" );
document.write( "            y = a(x²-3x-10)\r\n" );
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document.write( "ince it has y-intercept -10, when we set x=0, y equals -10\r\n" );
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document.write( "          -10 = a(0²-3·0-10)\r\n" );
document.write( "          -10 = a(-10)\r\n" );
document.write( "            1 = a\r\n" );
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document.write( "So the equation must be\r\n" );
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document.write( "            y = 1(x²-3x-10)\r\n" );
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document.write( "or just\r\n" );
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document.write( "            y = x²-3x-10\r\n" );
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document.write( "You can put this in vertex form to give a reason why it\r\n" );
document.write( "also has vertex (1.5,-12)\r\n" );
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document.write( "            y = x²-3x-10\r\n" );
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document.write( "Add 10 to both sides to get the -10 off the right side:\r\n" );
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document.write( "         y+10 = x²-3x\r\n" );
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document.write( "Complet the square on the right\r\n" );
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document.write( "1. Multiply the coefficient of x by 1/2, getting -3(1/2) = -1.5\\r\n" );
document.write( "2. Square this value (-1.5)² = 2.25\r\n" );
document.write( "3. Add that to both sides,\r\n" );
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document.write( "   y+10+2.25 = x²-3x+2.25\r\n" );
document.write( "     y+12.25 = (x-1.5)(x-1.5)\r\n" );
document.write( "     y+12.25 = (x-1.5)²\r\n" );
document.write( "           y = (x-1.5)²-12.25\r\n" );
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document.write( "Compare to\r\n" );
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document.write( "           y = a(x-h)²+k\r\n" );
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document.write( "So the vertex is (1.5,-12.25).\r\n" );
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document.write( "You must have meant that the vertex is (1.5,-12.25) not (1.5,12).\r\n" );
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document.write( "Here is the graph of the parabola with x-intercepts at 5 and -2,\r\n" );
document.write( "y-intecept at -10, and vertex (turning point at (1.5,-12.25)\r\n" );
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document.write( "So you see it crosses the x-axis at 5 and -2 and crosses the y-axis\r\n" );
document.write( "at -10.  However it has vertex (turning point) (1.5,-12.25).  \r\n" );
document.write( "So it had to be 12.25, not 12.  \r\n" );
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document.write( "Edwin

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