Exercise 4 Page 575

We want to order the given quadratic functions from widest to narrowest graph. y=- 2x^2, y=x^2, and y=- 0.25x^2 First, we will draw the graphs of the three functions on the same coordinate plane. Then we can compare the graphs. To graph them we will make a table of values for each function, including a variety of positive and negative inputs.

	y=- 2x^2		y=x^2		y=- 0.25x^2
x	- 2x^2	(x,y)	x^2	(x,y)	- 0.25x^2	(x,y)
- 2	- 2(- 2)^2	(- 2, - 8)	(- 2)^2	(- 2, 4)	- 0.25(- 2)^2	(- 2, - 1)
- 1	- 2(- 1)^2	(- 1, - 2)	(- 1)^2	(- 1, 1)	- 0.25(- 1)^2	(- 1, - 0.25)
	- 2( )^2	( , 0)	^2	( , 0)	- 0.25( )^2	( , 0)
1	- 2(1)^2	(1, - 2)	1^2	(1, 1)	- 0.25(1)^2	(1, - 0.25)
2	- 2(2)^2	(2, - 8)	2^2	(2, 4)	- 0.25(2)^2	(2, - 1)

Let's now draw the parabolas by plotting and connecting some of the obtained points.

Looking at the graphs, we can order the functions from widest to narrowest. y=- 0.25x^2, y=x^2, y=- 2x^2