A way to graph y=12(x−2)2+4 is to find the vertex and then create a table of values to graph. Since the equation is in vertex form (y=a(x−h)2+k), we know the vertex (h,k) is (2,4). This helps to focus on which x values to use, since the vertex must be in the middle.
Now to create a table: (choose an x value, plug it into the equation to find a y value)
(x,y)
x=0,y=12(0−2)2+4⇒y=12(−2)2+4⇒y=12(4)+4⇒y=2+4⇒y=6
(0,6)
x=1,y=12(1−2)2+4⇒y=12(−1)2+4⇒y=12(1)+4⇒y=12+4⇒y=4.5(412)
(1,4.5)
Vertex (2,4)
(the next values should match x=1 and x=0 since quadratics are symmetric)
x=3,y=12(3−2)2+4⇒y=12(1)2+4⇒y=12(1)+4⇒y=12+4⇒y=4.5(412)
(3,4.5)
x=4,y=12(4−2)2+4⇒y=12(2)2+4⇒y=12(4)+4⇒y=2+4⇒y=6
(4,6)
Now graph the following points:
(0,6),(1,4.5),(2,4),(3,4.5),(4,6)
Connect the dots, graph should be shaped as "u". That is the graph of the quadratic equation y=12(x−2)2+4.
