document.write( "Question 332279: I need help with this one please.
\n" ); document.write( "Graph the quadratic function
\n" ); document.write( "f(x)= 4(x+5)^2-1
\n" ); document.write( "Complete all of the steps required to find the information needed to be able to graph the function by hand.\r
\n" ); document.write( "\n" ); document.write( "Thank-you ahead of time. I sincerely appreciate your time. \n" ); document.write( "

Algebra.Com's Answer #238132 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "In order to graph $\"y=4%28x%2B5%29%5E2-1\"$ , we need to plot a few points.\r
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\n" ); document.write( "\n" ); document.write( "To get points in the form of (x,y), we need to find corresponding 'y' values to given 'x' values.\r
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\n" ); document.write( "\n" ); document.write( "Let's find the y value when $\"x=-7\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=4%28x%2B5%29%5E2-1\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=4%28-7%2B5%29%5E2-1\"$ Plug in $\"x=-7\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=4%28-2%29%5E2-1\"$ Add -7 to 5 to get -2.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=4%284%29-1\"$ Square -2 to get 4.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=16-1\"$ Multiply 4 and 4 to get 16 .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=15\"$ Subtract 1 from 16 to get 15 .\r
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\n" ); document.write( "\n" ); document.write( "So if $\"x=-7\"$ , then $\"y=15\"$ which gives us the point (-7,15).\r
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\n" ); document.write( "\n" ); document.write( "Let's find the y value when $\"x=-6\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=4%28x%2B5%29%5E2-1\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=4%28-6%2B5%29%5E2-1\"$ Plug in $\"x=-6\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=4%28-1%29%5E2-1\"$ Add -6 to 5 to get -1.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=4%281%29-1\"$ Square -1 to get 1.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=4-1\"$ Multiply 4 and 1 to get 4 .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=3\"$ Subtract 1 from 4 to get 3 .\r
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\n" ); document.write( "\n" ); document.write( "So if $\"x=-6\"$ , then $\"y=3\"$ which gives us the point (-6,3).\r
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\n" ); document.write( "\n" ); document.write( "Let's find the y value when $\"x=-5\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=4%28x%2B5%29%5E2-1\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=4%28-5%2B5%29%5E2-1\"$ Plug in $\"x=-5\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=4%280%29%5E2-1\"$ Add -5 to 5 to get 0.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=4%280%29-1\"$ Square 0 to get 0.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=0-1\"$ Multiply 4 and 0 to get 0 .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=-1\"$ Subtract 1 from 0 to get -1 .\r
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\n" ); document.write( "\n" ); document.write( "So if $\"x=-5\"$ , then $\"y=-1\"$ which gives us the point (-5,-1).\r
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\n" ); document.write( "\n" ); document.write( "Let's find the y value when $\"x=-4\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=4%28x%2B5%29%5E2-1\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=4%28-4%2B5%29%5E2-1\"$ Plug in $\"x=-4\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=4%281%29%5E2-1\"$ Add -4 to 5 to get 1.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=4%281%29-1\"$ Square 1 to get 1.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=4-1\"$ Multiply 4 and 1 to get 4 .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=3\"$ Subtract 1 from 4 to get 3 .\r
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\n" ); document.write( "\n" ); document.write( "So if $\"x=-4\"$ , then $\"y=3\"$ which gives us the point (-4,3).\r
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\n" ); document.write( "\n" ); document.write( "Let's find the y value when $\"x=-3\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=4%28x%2B5%29%5E2-1\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=4%28-3%2B5%29%5E2-1\"$ Plug in $\"x=-3\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=4%282%29%5E2-1\"$ Add -3 to 5 to get 2.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=4%284%29-1\"$ Square 2 to get 4.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=16-1\"$ Multiply 4 and 4 to get 16 .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=15\"$ Subtract 1 from 16 to get 15 .\r
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\n" ); document.write( "\n" ); document.write( "So if $\"x=-3\"$ , then $\"y=15\"$ which gives us the point (-3,15).\r
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\n" ); document.write( "\n" ); document.write( "Now let's make a table of the values we just found.\r
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Table of Values:

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document.write( "x y
-7 15
-6 3
-5 -1
-4 3
-3 15\r\n" );
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\n" ); document.write( "\n" ); document.write( "Now let's plot the points:\r
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Graph:

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\n" ); document.write( "\n" ); document.write( "Now draw a curve through all of the points to graph $\"y=4%28x%2B5%29%5E2-1\"$ :\r
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Graph of $\"y=4%28x%2B5%29%5E2-1\"$ \n" ); document.write( "

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