document.write( "Question 122811: Graph the equation\r
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Algebra.Com's Answer #90185 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
# 1\r
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\n" ); document.write( "\n" ); document.write( "In order to graph $\"f%28x%29=-1x%5E2%2B1\"$ , we need to plot some points. To do that, we need to plug in some x values to get some y values\r
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\n" ); document.write( "\n" ); document.write( "So let's find the first point:\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=-1x%5E2%2B1\"$ Start with the given function\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-3%29=-1%28-3%29%5E2%2B1\"$ Plug in $\"x=-3\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-3%29=-1%2A9%2B1\"$ Raise -3 to the 2nd power to get 9\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-3%29=-9%2B1\"$ Multiply -1 and 9 to get -9\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-3%29=-8\"$ Add -9 and 1 to get -8\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=-3\"$ , we have $\"y=-8\"$ \r
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\n" ); document.write( "\n" ); document.write( "So our 1st point is (-3,-8)\r
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\n" ); document.write( "\n" ); document.write( "-------------- Let's find another point --------------\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=-1x%5E2%2B1\"$ Start with the given function\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-2%29=-1%28-2%29%5E2%2B1\"$ Plug in $\"x=-2\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-2%29=-1%2A4%2B1\"$ Raise -2 to the 2nd power to get 4\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-2%29=-4%2B1\"$ Multiply -1 and 4 to get -4\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-2%29=-3\"$ Add -4 and 1 to get -3\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=-2\"$ , we have $\"y=-3\"$ \r
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\n" ); document.write( "\n" ); document.write( "So our 2nd point is (-2,-3)\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=-1x%5E2%2B1\"$ Start with the given function\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-1%29=-1%28-1%29%5E2%2B1\"$ Plug in $\"x=-1\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-1%29=-1%2A1%2B1\"$ Raise -1 to the 2nd power to get 1\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-1%29=-1%2B1\"$ Multiply -1 and 1 to get -1\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-1%29=0\"$ Add -1 and 1 to get 0\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=-1\"$ , we have $\"y=0\"$ \r
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\n" ); document.write( "\n" ); document.write( "So our 3rd point is (-1,0)\r
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\n" ); document.write( "\n" ); document.write( "-------------- Let's find another point --------------\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=-1x%5E2%2B1\"$ Start with the given function\r
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\n" ); document.write( "\n" ); document.write( " $\"f%280%29=-1%280%29%5E2%2B1\"$ Plug in $\"x=0\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%280%29=-1%2A0%2B1\"$ Raise 0 to the 2nd power to get 0\r
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\n" ); document.write( "\n" ); document.write( " $\"f%280%29=0%2B1\"$ Multiply -1 and 0 to get 0\r
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\n" ); document.write( "\n" ); document.write( " $\"f%280%29=1\"$ Add 0 and 1 to get 1\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=0\"$ , we have $\"y=1\"$ \r
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\n" ); document.write( "\n" ); document.write( "So our 4th point is (0,1)\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=-1x%5E2%2B1\"$ Start with the given function\r
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\n" ); document.write( "\n" ); document.write( " $\"f%281%29=-1%281%29%5E2%2B1\"$ Plug in $\"x=1\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%281%29=-1%2A1%2B1\"$ Raise 1 to the 2nd power to get 1\r
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\n" ); document.write( "\n" ); document.write( " $\"f%281%29=-1%2B1\"$ Multiply -1 and 1 to get -1\r
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\n" ); document.write( "\n" ); document.write( " $\"f%281%29=0\"$ Add -1 and 1 to get 0\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=1\"$ , we have $\"y=0\"$ \r
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\n" ); document.write( "\n" ); document.write( "So our 5th point is (1,0)\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=-1x%5E2%2B1\"$ Start with the given function\r
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\n" ); document.write( "\n" ); document.write( " $\"f%282%29=-1%282%29%5E2%2B1\"$ Plug in $\"x=2\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%282%29=-1%2A4%2B1\"$ Raise 2 to the 2nd power to get 4\r
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\n" ); document.write( "\n" ); document.write( " $\"f%282%29=-4%2B1\"$ Multiply -1 and 4 to get -4\r
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\n" ); document.write( "\n" ); document.write( " $\"f%282%29=-3\"$ Add -4 and 1 to get -3\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=2\"$ , we have $\"y=-3\"$ \r
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\n" ); document.write( "\n" ); document.write( "So our 6th point is (2,-3)\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=-1x%5E2%2B1\"$ Start with the given function\r
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\n" ); document.write( "\n" ); document.write( " $\"f%283%29=-1%283%29%5E2%2B1\"$ Plug in $\"x=3\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%283%29=-1%2A9%2B1\"$ Raise 3 to the 2nd power to get 9\r
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\n" ); document.write( "\n" ); document.write( " $\"f%283%29=-9%2B1\"$ Multiply -1 and 9 to get -9\r
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\n" ); document.write( "\n" ); document.write( " $\"f%283%29=-8\"$ Add -9 and 1 to get -8\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=3\"$ , we have $\"y=-8\"$ \r
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\n" ); document.write( "\n" ); document.write( "So our 7th point is (3,-8)\r
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\n" ); document.write( "\n" ); document.write( "Now lets make a table of the values we have calculated\r
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document.write( " x y
 -3 -8
 -2 -3
 -1 0
 0 1
 1 0
 2 -3
 3 -8\r\n" );
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Now plot the points\r
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\r
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\n" ); document.write( "\n" ); document.write( "Now connect the points to graph $\"y=-1x%5E2%2B1\"$ (note: the more points you plot, the easier it is to draw the graph)\r
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\n" ); document.write( "\n" ); document.write( "Looking at $\"y=2x\"$ we can see that the equation is in slope-intercept form $\"y=mx%2Bb\"$ where the slope is $\"m=2\"$ and the y-intercept is $\"b=0\"$ note: $\"y=2x\"$ really looks like $\"y=2x%2B0\"$ \r
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\n" ); document.write( "\n" ); document.write( "Since $\"b=0\"$ this tells us that the y-intercept is

.Remember the y-intercept is the point where the graph intersects with the y-axis\r
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\r
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\r
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\n" ); document.write( "\n" ); document.write( "Now since the slope is comprised of the \"rise\" over the \"run\" this means\r
\n" ); document.write( "\n" ); document.write( " $\"slope=rise%2Frun\"$ \r
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\n" ); document.write( "\n" ); document.write( "Also, because the slope is $\"2\"$ , this means:\r
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\n" ); document.write( "\n" ); document.write( " $\"rise%2Frun=2%2F1\"$ \r
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\n" ); document.write( "\n" ); document.write( "which shows us that the rise is 2 and the run is 1. This means that to go from point to point, we can go up 2 and over 1\r
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, go up 2 units \r
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\r
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\n" ); document.write( "\n" ); document.write( "and to the right 1 unit to get to the next point

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\r
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\n" ); document.write( "\n" ); document.write( "Now draw a line through these points to graph $\"y=2x\"$ \r
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So this is the graph of $\"y=2x\"$ through the points

and

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