document.write( "Question 118550: sketch the graph of the function. label the coordinates of the vertex. make sure to make your x & y table. then plot the points on the graph.\r
\n" ); document.write( "\n" ); document.write( "1) y=-x^2-4x+2\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "solve the equation algebraically. check your solution by graphing. make sure to use an x &y table.
\n" ); document.write( "2)x^2-4=12 \n" ); document.write( "
Algebra.Com's Answer #86815 by ankor@dixie-net.com(22740)\"\" \"About 
You can put this solution on YOUR website!
sketch the graph of the function. label the coordinates of the vertex. make sure to make your x & y table. then plot the points on the graph.
\n" ); document.write( "1) y = -x^2 - 4x + 2
\n" ); document.write( ":
\n" ); document.write( "First find the axis of symmetry (x= -b/(2a)) find the vertex from that and it
\n" ); document.write( "helps you choose the values for x when you make your x/y tables
\n" ); document.write( ":
\n" ); document.write( "In this equation: a = -1; b = -4
\n" ); document.write( "x =\"%28-%28-4%29%29%2F%282%2A-1%29\" = \"4%2F-2\" = -2 is the axis of symmetry
\n" ); document.write( ":
\n" ); document.write( "Find the vertex, substitute -2 for x in the original equation:
\n" ); document.write( "y = -1(-2^2) - 4(-2) + 2
\n" ); document.write( "y = -4 + 8 + 2
\n" ); document.write( "y = +6
\n" ); document.write( ":
\n" ); document.write( "Vertex is -2,+6
\n" ); document.write( ":
\n" ); document.write( "Choose the x values above and below x = -2
\n" ); document.write( "Substitute each value for x in the equation, you should get table like this
\n" ); document.write( " x | y
\n" ); document.write( "-------
\n" ); document.write( "-5 |-3
\n" ); document.write( "-3 |+5
\n" ); document.write( "-2 |+6; the vertex
\n" ); document.write( "-1 |+5
\n" ); document.write( " 0 |+2; the y intercept
\n" ); document.write( "+1 |-3
\n" ); document.write( ":
\n" ); document.write( "Plot these x/y coordinates and your graph should look like this:
\n" ); document.write( ":
\n" ); document.write( "\"+graph%28+300%2C+200%2C+-6%2C+4%2C+-6%2C+10%2C+-x%5E2-4x%2B2%29+\"
\n" ); document.write( "You can label the coordinates of the vertex: -2,+6
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "solve the equation algebraically. check your solution by graphing. make sure to use an x &y table.
\n" ); document.write( "2)
\n" ); document.write( "x^2 - 4 = 12
\n" ); document.write( ":
\n" ); document.write( "x^2 - 4 - 12 = 0; subtracted 12 from both sides:
\n" ); document.write( ":
\n" ); document.write( "x^2 - 16 = 0; recognize this as the \"difference of squares\"
\n" ); document.write( ":
\n" ); document.write( "Factors to:
\n" ); document.write( "(x-4)(x+4) = 0
\n" ); document.write( ":
\n" ); document.write( "x = +4 and x = -4
\n" ); document.write( ":
\n" ); document.write( "Make a table from x = -5 to +5, this will include the x intercepts
\n" ); document.write( " x| y
\n" ); document.write( "------
\n" ); document.write( "-5|+9
\n" ); document.write( "-4| 0; x intercept
\n" ); document.write( "-2|-12
\n" ); document.write( "0 |-16; the vertex
\n" ); document.write( "+2|-12
\n" ); document.write( "+4| 0; x intercept
\n" ); document.write( "+5|+9
\n" ); document.write( ":
\n" ); document.write( "Plot these and the graph should look like this:
\n" ); document.write( "\"+graph%28+300%2C+200%2C+-6%2C+6%2C+-20%2C+10%2C+x%5E2-16%29+\"
\n" ); document.write( ":
\n" ); document.write( "Did this help? Any questions? \n" ); document.write( "
\n" );