document.write( "Question 124293: Can you please help with this problem from college algebra blitzer.using this function f(x) =x^2 +4x +1, find h, the x-coordinate of the vertex of this parabola,using a graph.\r
\n" ); document.write( "\n" ); document.write( "substitute the two intergers immediately to the left and right of h into the function to find the corresponding y. fill in following table. make sure the x- values are in increasing order in your table.\r
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Algebra.Com's Answer #91096 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
To find h, use this formula:\r
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\n" ); document.write( "\n" ); document.write( " $\"h=-b%2F%282a%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "From the equation $\"y=x%5E2%2B4x%2B1\"$ we can see that a=1 and b=4\r
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\n" ); document.write( "\n" ); document.write( " $\"h=%28-4%29%2F%282%2A1%29\"$ Plug in b=4 and a=1\r
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\n" ); document.write( "\n" ); document.write( " $\"h=%28-4%29%2F2\"$ Multiply 2 and 1 to get 2\r
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\n" ); document.write( "\n" ); document.write( " $\"h=-2\"$ Reduce\r
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\n" ); document.write( "\n" ); document.write( "So the axis of symmetry is $\"x=-2\"$ \r
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\n" ); document.write( "\n" ); document.write( "So the x-coordinate of the vertex is $\"x=-2\"$ . Lets plug this into the equation to find the y-coordinate of the vertex.\r
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\n" ); document.write( "\n" ); document.write( "Lets evaluate $\"f%28-2%29\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=x%5E2%2B4x%2B1\"$ Start with the given polynomial\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-2%29=%28-2%29%5E2%2B4%28-2%29%2B1\"$ Plug in $\"x=-2\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-2%29=%284%29%2B4%28-2%29%2B1\"$ Raise -2 to the second power to get 4\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-2%29=%284%29%2B-8%2B1\"$ Multiply 4 by -2 to get -8\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-2%29=-3\"$ Now combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So the vertex is (-2,-3)\r
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\n" ); document.write( "\n" ); document.write( "Now lets find 2 other points to the left of the vertex\r
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\n" ); document.write( "\n" ); document.write( "Lets evaluate $\"f%28-4%29\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=x%5E2%2B4x%2B1\"$ Start with the given polynomial\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-4%29=%28-4%29%5E2%2B4%28-4%29%2B1\"$ Plug in $\"x=-4\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-4%29=%2816%29%2B4%28-4%29%2B1\"$ Raise -4 to the second power to get 16\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-4%29=%2816%29%2B-16%2B1\"$ Multiply 4 by -4 to get -16\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-4%29=1\"$ Now combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So our 1st point is (-4,1)\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( "Lets evaluate $\"f%28-3%29\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=x%5E2%2B4x%2B1\"$ Start with the given polynomial\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-3%29=%28-3%29%5E2%2B4%28-3%29%2B1\"$ Plug in $\"x=-3\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-3%29=%289%29%2B4%28-3%29%2B1\"$ Raise -3 to the second power to get 9\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-3%29=%289%29%2B-12%2B1\"$ Multiply 4 by -3 to get -12\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-3%29=-2\"$ Now combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So our 2nd point is (-3,-2)\r
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\n" ); document.write( "\n" ); document.write( "Now remember, the parabola is symmetrical about the axis of symmetry (which is $\"x=-2\"$ )\r
\n" ); document.write( "\n" ); document.write( "This means the y-value for $\"x=-3\"$ is equal to the y-value of $\"x=-1\"$ . So when $\"x=-1\"$ , $\"y=-2\"$ .\r
\n" ); document.write( "\n" ); document.write( "Also, the y-value for $\"x=-4\"$ is equal to the y-value of $\"x=0\"$ . So when $\"x=0\"$ , $\"y=1\"$ .\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
 -4 1
 -3 -2
 -2 -3
 -1 -2
 0 1\r\n" );
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\n" ); document.write( "\n" ); document.write( "Now let's plot these points to graph $\"y=x%5E2%2B4x%2B1\"$ \r
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