document.write( "Question 87018: Sketch the graph of the following functions
\n" ); document.write( "h(x) = -x^2 + 2 \n" ); document.write( "

Algebra.Com's Answer #62977 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
In order to graph $\"y=-x%5E2%2B2\"$ , we need to plot some points.
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\n" ); document.write( "\n" ); document.write( " $\"h%28x%29=-x%5E2%2B2\"$ Start with the given polynomial \r
\n" ); document.write( "\n" ); document.write( " $\"h%28-3%29=-%28-3%29%5E2%2B2\"$ Plug in $\"x=-3\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"h%28-3%29=-7\"$ Evaluate the expression by following the order of operations\r
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\n" ); document.write( "\n" ); document.write( "So our first point is (-3,-7)\r
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\n" ); document.write( "\n" ); document.write( "----Now lets find another point----\r
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\n" ); document.write( "\n" ); document.write( " $\"h%28x%29=-x%5E2%2B2\"$ Start with the given polynomial \r
\n" ); document.write( "\n" ); document.write( " $\"h%28-2%29=-%28-2%29%5E2%2B2\"$ Plug in $\"x=-2\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"h%28-2%29=-2\"$ Evaluate the expression by following the order of operations\r
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\n" ); document.write( "\n" ); document.write( "So our second point is (-2,-2)\r
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\n" ); document.write( "\n" ); document.write( "----Now lets find another point----\r
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\n" ); document.write( "\n" ); document.write( " $\"h%28x%29=-x%5E2%2B2\"$ Start with the given polynomial \r
\n" ); document.write( "\n" ); document.write( " $\"h%28-1%29=-%28-1%29%5E2%2B2\"$ Plug in $\"x=-1\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"h%28-1%29=1\"$ Evaluate the expression by following the order of operations\r
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\n" ); document.write( "\n" ); document.write( "So our third point is (-1,1)\r
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\n" ); document.write( "\n" ); document.write( "----Now lets find another point----\r
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\n" ); document.write( "\n" ); document.write( " $\"h%28x%29=-x%5E2%2B2\"$ Start with the given polynomial \r
\n" ); document.write( "\n" ); document.write( " $\"h%280%29=-%280%29%5E2%2B2\"$ Plug in $\"x=0\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"h%280%29=2\"$ Evaluate the expression by following the order of operations\r
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\n" ); document.write( "\n" ); document.write( "So our fourth point is (0,2)\r
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\n" ); document.write( "\n" ); document.write( "----Now lets find another point----\r
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\n" ); document.write( "\n" ); document.write( " $\"h%28x%29=-x%5E2%2B2\"$ Start with the given polynomial \r
\n" ); document.write( "\n" ); document.write( " $\"h%281%29=-%281%29%5E2%2B2\"$ Plug in $\"x=1\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"h%281%29=1\"$ Evaluate the expression by following the order of operations\r
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\n" ); document.write( "\n" ); document.write( "So our fifth point is (1,1)\r
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\n" ); document.write( "\n" ); document.write( "----Now lets find another point----\r
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\n" ); document.write( "\n" ); document.write( " $\"h%28x%29=-x%5E2%2B2\"$ Start with the given polynomial \r
\n" ); document.write( "\n" ); document.write( " $\"h%282%29=-%282%29%5E2%2B2\"$ Plug in $\"x=2\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"h%282%29=-2\"$ Evaluate the expression by following the order of operations\r
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\n" ); document.write( "\n" ); document.write( "So our sixth point is (2,-2)\r
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\n" ); document.write( "\n" ); document.write( "----Now lets find another point----\r
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\n" ); document.write( "\n" ); document.write( " $\"h%28x%29=-x%5E2%2B2\"$ Start with the given polynomial \r
\n" ); document.write( "\n" ); document.write( " $\"h%283%29=-%283%29%5E2%2B2\"$ Plug in $\"x=3\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"h%283%29=-7\"$ Evaluate the expression by following the order of operations\r
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\n" ); document.write( "\n" ); document.write( "So our seventh point is (3,-7)\r
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\n" ); document.write( "\n" ); document.write( "----Now lets find another point----\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 -7
 -2 -2
 -1 1
 0 2
 1 1
 2 -2
 3 -7\r\n" );
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Now plot the points\r
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\n" ); document.write( "\n" ); document.write( "Now connect the points to graph $\"y=-x%5E2%2B2\"$ \r
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