Quadratic Homework -- Graphing Quadratic Functions 1.1 2008/05/28 15:53:03.011 GMT-5 2009/01/07 16:24:54.930 US/Central Kenny Felder KFelder@RaleighCharterHS.org Kenny Felder KFelder@RaleighCharterHS.org algebra equations functions graphing quadratic equations quadratics An introduction to graphing quadratic functions. Graph by plotting points. Make sure to include positive and negative values of x size 12{x} {}! y=x2 size 12{y=x rSup { size 8{2} } } {} x size 12{x} {} y size 12{y} {} Note that there is a little point at the bottom of the graph. This point is called the “vertex.” Graph each of the following by drawing these as variations of #1—that is, by seeing how the various numbers transform the graph of y = x 2 size 12{y=x rSup { size 8{2} } } {} . Next to each one, write down the coordinates of the vertex. y = x 2 + 3 size 12{y=x rSup { size 8{2} } +3} {} Vertex: y = x 2 − 3 size 12{y=x rSup { size 8{2} } - 3} {} Vertex: y = ( x − 5 ) 2 size 12{y= \( x - 5 \) rSup { size 8{2} } } {} Vertex: Plot a few points to verify that your graph of #4 is correct. y=(x+5)2 size 12{y= \( x+5 \) rSup { size 8{2} } } {} Vertex: y = 2x 2 size 12{y=2x rSup { size 8{2} } } {} Vertex: y=12x2 size 12{y= { {1} over {2} } x rSup { size 8{2} } } {} Vertex: y = − x 2 size 12{y= - x rSup { size 8{2} } } {} Vertex: In these graphs, each problem transforms the graph in several different ways. y = ( x − 5 ) 2 − 3 size 12{y= \( x - 5 \) rSup { size 8{2} } - 3} {} Vertex: Make a graph on the calculator to verify that your graph of #10 is correct. y = 2 ( x − 5 ) 2 − 3 size 12{y=2 \( x - 5 \) rSup { size 8{2} } - 3} {} Vertex: y = − 2 ( x − 5 ) 2 − 3 size 12{y= - 2 \( x - 5 \) rSup { size 8{2} } - 3} {} Vertex: y = 1 2 ( x + 5 ) 2 + 3 size 12{y= { {1} over {2} } \( x+5 \) rSup { size 8{2} } +3} {} Vertex: Where is the vertex of the general graph y=a(x−h)2+k size 12{y=a \( x - h \) rSup { size 8{2} } +k} {}? Graph by plotting points. Make sure to include positive and negative values of y size 12{y} {}! x=y2 size 12{x=y rSup { size 8{2} } } {} y size 12{y} {} x size 12{x} {} Graph by drawing these as variations of #16—that is, by seeing how the various numbers transform the graph of x=y2 size 12{x=y rSup { size 8{2} } } {}. x = y 2 + 4 size 12{x=y rSup { size 8{2} } +4} {} x = ( y − 2 ) 2 size 12{x= \( y - 2 \) rSup { size 8{2} } } {} Plot a few points to verify that your graph of #18 is correct. x = − y 2 size 12{x= - y rSup { size 8{2} } } {} x = − 2 ( y − 2 ) 2 + 4 size 12{x= - 2 \( y - 2 \) rSup { size 8{2} } +4} {}