Page 3a

PRELIMINARIES Menu

MAIN MENU

EXAMPLE
Sketch the parabola defined by y = (1/4)(x - 6)2 + 3.
You might recall that, given the above equation, you can immediatly pick out the vertex of the parabola. In this case the vertex is (6, 3).
This is important information, but let's plot the graph as if we didn't know this information and see what we can discover.
First, let's look at the effect of the scaling factor 1/4 on the graph of y = x2. That is, let's graph the parabola defined by the equation y = (1/4)x2.

x	y = x2	y = (1/4)x2
	0	0	0
	1	1	0.25
	-1	1	0.25
	2	4	1
	-2	4	1
	5	25	6.25
	-5	25	6.25

Notice that multiplying the x2 by (1/4) makes the graph of the parabola wider.

Now let's look at the effect of the 6 and the 3 in the equation y = (1/4)(x - 6)2 + 3.

First we will plot y = (1/4)x2 + 3, to see this effect. See the black graph below.

x	y = (1/4)x2	y = (1/4)x2 + 3
	0	0	3
	1	0.25	3.25
	-1	0.25	3.25
	2	1	4
	-2	1	4
	5	6.25	9.25
	-5	6.25	9.25

We can see above that the effect of the + 3 shifts the graph 3 units upwards. (Note: Despite the optical illusion, this graph is uniformily shifted up by 3.)

Now let's look at the effect of the - 6 on the graph.

The blue graph illustrates the effect of the (x - 6) in the equation y = (1/4)(x - 6)2 + 3.

x	x - 6	y = (1/4)(x - 6)2 + 3
	6	0	3
	7	1	3.25
	5	-1	3.25
	8	2	4
	4	-2	4
	11	5	9.25
	1	-5	9.25