Exercise 1 Page 575

We want to order the given quadratic functions from widest to narrowest graph. y=2x^2, y=0.5x^2, and y=- x^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=0.5x^2		y=- x^2
x	2x^2	(x,y)	0.5x^2	(x,y)	- x^2	(x,y)
- 2	2(- 2)^2	(- 2, 8)	0.5(- 2)^2	(- 2, 2)	-(- 2)^2	(- 2, - 4)
- 1	2(- 1)^2	(- 1, 2)	0.5(- 1)^2	(- 1, 0.5)	- (- 1)^2	(- 1, - 1)
	2( )^2	( , 0)	0.5( )^2	( , 0)	- ( )^2	( , 0)
1	2(1)^2	(1, 2)	0.5(1)^2	(1, 0.5)	-(1)^2	(1, - 1)
2	2(2)^2	(2, 8)	0.5(2)^2	(2, 2)	-(2)^2	(2, - 4)

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. y=0.5x^2, y=- x^2, y=2x^2