Graph all three functions on the same coordinate plane. Then compare the graphs.
y=0.5x^2, y=- x^2, y=2x^2
Practice makes perfect
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
