Exercise 3 Page 575

We want to order the given quadratic functions from widest to narrowest graph. f(x)=0.6x^2, f(x)=0.3x^2, and f(x)=0.2x^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.

	f(x)=0.6x^2		f(x)=0.3x^2		f(x)=0.2x^2
x	0.6x^2	(x,y)	0.3x^2	(x,y)	0.2x^2	(x,y)
- 2	0.6(- 2)^2	(- 2, 2.4)	0.3(- 2)^2	(- 2, 1.2)	0.2(- 2)^2	(- 2, 0.8)
- 1	0.6(- 1)^2	(- 1, 0.6)	0.3(- 1)^2	(- 1, 0.3)	0.2(- 1)^2	(- 1, 0.2)
	0.6( )^2	( , 0)	0.3( )^2	( , 0)	0.2( )^2	( , 0)
1	0.6(1)^2	(1, 0.6)	0.3(1)^2	(1, 0.3)	0.2(1)^2	(1, 0.2)
2	0.6(2)^2	(2, 2.4)	0.3(2)^2	(2, 1.2)	0.2(2)^2	(2, 0.8)

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

Looking at the graphs, we can order the functions from widest to narrowest. f(x)=0.2x^2, f(x)=0.3x^2, f(x)=0.6x^2