document.write( "Question 86559: Hi thank
\n" ); document.write( " you Cecilia, for the solution to my other problem, Here is another one I am not sure of: Use several points to graph. If f(x)= xsquared - 5x + 11. Find f(-3). I have an answer of 17, but am not sure. Thank you for your much needed help \n" ); document.write( "

Algebra.Com's Answer #62602 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
In order to graph $\"y=x%5E2-5x%2B11\"$ , we need to plot some points.
\n" ); document.write( " So we can start at any x value. So lets start at x=-5
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\n" ); document.write( "\n" ); document.write( " $\"y=x%5E2-5x%2B11\"$ Start with the given equation
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\n" ); document.write( " $\"y=%28-5%29%5E2-5%28-5%29%2B11\"$ Plug in $\"x=-5\"$
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\n" ); document.write( " $\"%28-5%29%5E2-5%28-5%29%2B11=61\"$ Calculate the y value by following the order of operations\r
\n" ); document.write( "\n" ); document.write( "So when $\"x=-5\"$ $\"y=61\"$ \r
\n" ); document.write( "\n" ); document.write( "So our 1st point is (-5,61)\r
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\n" ); document.write( "\n" ); document.write( "Now lets find another point
\n" ); document.write( " $\"y=x%5E2-5x%2B11\"$ Start with the given equation
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\n" ); document.write( " $\"y=%28-4%29%5E2-5%28-4%29%2B11\"$ Plug in $\"x=-4\"$
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\n" ); document.write( " $\"%28-4%29%5E2-5%28-4%29%2B11=47\"$ Calculate the y value by following the order of operations\r
\n" ); document.write( "\n" ); document.write( "So when $\"x=-4\"$ $\"y=47\"$ \r
\n" ); document.write( "\n" ); document.write( "So our 2nd point is (-4,47)\r
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\n" ); document.write( "\n" ); document.write( "Now lets find another point
\n" ); document.write( " $\"y=x%5E2-5x%2B11\"$ Start with the given equation
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\n" ); document.write( " $\"y=%28-3%29%5E2-5%28-3%29%2B11\"$ Plug in $\"x=-3\"$
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\n" ); document.write( " $\"%28-3%29%5E2-5%28-3%29%2B11=35\"$ Calculate the y value by following the order of operations\r
\n" ); document.write( "\n" ); document.write( "So when $\"x=-3\"$ $\"y=35\"$ \r
\n" ); document.write( "\n" ); document.write( "So our 3rd point is (-3,35)\r
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\n" ); document.write( "\n" ); document.write( "Now lets find another point
\n" ); document.write( " $\"y=x%5E2-5x%2B11\"$ Start with the given equation
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\n" ); document.write( " $\"y=%28-2%29%5E2-5%28-2%29%2B11\"$ Plug in $\"x=-2\"$
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\n" ); document.write( " $\"%28-2%29%5E2-5%28-2%29%2B11=25\"$ Calculate the y value by following the order of operations\r
\n" ); document.write( "\n" ); document.write( "So when $\"x=-2\"$ $\"y=25\"$ \r
\n" ); document.write( "\n" ); document.write( "So our 4th point is (-2,25)\r
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\n" ); document.write( "\n" ); document.write( "Now lets find another point
\n" ); document.write( " $\"y=x%5E2-5x%2B11\"$ Start with the given equation
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\n" ); document.write( " $\"y=%28-1%29%5E2-5%28-1%29%2B11\"$ Plug in $\"x=-1\"$
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\n" ); document.write( " $\"%28-1%29%5E2-5%28-1%29%2B11=17\"$ Calculate the y value by following the order of operations\r
\n" ); document.write( "\n" ); document.write( "So when $\"x=-1\"$ $\"y=17\"$ \r
\n" ); document.write( "\n" ); document.write( "So our 5th point is (-1,17)\r
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\n" ); document.write( "\n" ); document.write( "Now lets find another point
\n" ); document.write( " $\"y=x%5E2-5x%2B11\"$ Start with the given equation
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\n" ); document.write( " $\"y=%280%29%5E2-5%280%29%2B11\"$ Plug in $\"x=0\"$
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\n" ); document.write( " $\"%280%29%5E2-5%280%29%2B11=11\"$ Calculate the y value by following the order of operations\r
\n" ); document.write( "\n" ); document.write( "So when $\"x=0\"$ $\"y=11\"$ \r
\n" ); document.write( "\n" ); document.write( "So our 6th point is (0,11)\r
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\n" ); document.write( "\n" ); document.write( "Now lets find another point
\n" ); document.write( " $\"y=x%5E2-5x%2B11\"$ Start with the given equation
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\n" ); document.write( " $\"y=%281%29%5E2-5%281%29%2B11\"$ Plug in $\"x=1\"$
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\n" ); document.write( " $\"%281%29%5E2-5%281%29%2B11=7\"$ Calculate the y value by following the order of operations\r
\n" ); document.write( "\n" ); document.write( "So when $\"x=1\"$ $\"y=7\"$ \r
\n" ); document.write( "\n" ); document.write( "So our 7th point is (1,7)\r
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\n" ); document.write( "\n" ); document.write( "Now lets find another point
\n" ); document.write( " $\"y=x%5E2-5x%2B11\"$ Start with the given equation
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\n" ); document.write( " $\"y=%282%29%5E2-5%282%29%2B11\"$ Plug in $\"x=2\"$
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\n" ); document.write( " $\"%282%29%5E2-5%282%29%2B11=5\"$ Calculate the y value by following the order of operations\r
\n" ); document.write( "\n" ); document.write( "So when $\"x=2\"$ $\"y=5\"$ \r
\n" ); document.write( "\n" ); document.write( "So our 8th point is (2,5)\r
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\n" ); document.write( "\n" ); document.write( "Now lets find another point
\n" ); document.write( " $\"y=x%5E2-5x%2B11\"$ Start with the given equation
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\n" ); document.write( " $\"y=%283%29%5E2-5%283%29%2B11\"$ Plug in $\"x=3\"$
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\n" ); document.write( " $\"%283%29%5E2-5%283%29%2B11=5\"$ Calculate the y value by following the order of operations\r
\n" ); document.write( "\n" ); document.write( "So when $\"x=3\"$ $\"y=5\"$ \r
\n" ); document.write( "\n" ); document.write( "So our 9th point is (3,5)\r
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\n" ); document.write( "\n" ); document.write( "Now lets find another point
\n" ); document.write( " $\"y=x%5E2-5x%2B11\"$ Start with the given equation
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\n" ); document.write( " $\"y=%284%29%5E2-5%284%29%2B11\"$ Plug in $\"x=4\"$
\n" ); document.write( "
\n" ); document.write( " $\"%284%29%5E2-5%284%29%2B11=7\"$ Calculate the y value by following the order of operations\r
\n" ); document.write( "\n" ); document.write( "So when $\"x=4\"$ $\"y=7\"$ \r
\n" ); document.write( "\n" ); document.write( "So our 10th point is (4,7)\r
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\n" ); document.write( "\n" ); document.write( "Now lets find another point
\n" ); document.write( " $\"y=x%5E2-5x%2B11\"$ Start with the given equation
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\n" ); document.write( " $\"y=%285%29%5E2-5%285%29%2B11\"$ Plug in $\"x=5\"$
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\n" ); document.write( " $\"%285%29%5E2-5%285%29%2B11=11\"$ Calculate the y value by following the order of operations\r
\n" ); document.write( "\n" ); document.write( "So when $\"x=5\"$ $\"y=11\"$ \r
\n" ); document.write( "\n" ); document.write( "So our 11th point is (5,11)\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
 -5 61
 -4 47
 -3 35
 -2 25
 -1 17
 0 11
 1 7
 2 5
 3 5
 4 7
 5 11\r\n" );
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Now plot the points\r
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\r
\n" ); document.write( "\n" ); document.write( "Now connect the points, this is the graph of $\"y=x%5E2-5x%2B11\"$ \r
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\r
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\n" ); document.write( "\n" ); document.write( "So by looking at the table, we can see that $\"f%28-3%29=35\"$ . You were close. I'm assuming you calculated\r
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\n" ); document.write( "\n" ); document.write( " $\"-3%5E2-5%2A-3%2B11=-9%2B15%2B11=17\"$ you only squared the 3 and not the negative\r
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\n" ); document.write( "\n" ); document.write( "where you should have done this (note: I'm squaring the negative also. So it goes from -3 to 9)\r
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\n" ); document.write( "\n" ); document.write( " $\"%28-3%29%5E2-5%2A-3%2B11=9%2B15%2B11=35\"$
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