We want to order the given quadratic functions from widest to narrowest graph.
y=-1/2x^2, y=5x^2, and y=-1/4x^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=-1/2x^2
y=5x^2
y=-1/4x^2
x
-1/2x^2
(x,y)
5x^2
(x,y)
-1/4x^2
(x,y)
- 2
-1/2( - 2)^2
( - 2, - 2)
5( - 2)^2
( - 2, 20)
-1/4( - 2)^2
( - 2, -1)
- 1
-1/2( - 1)^2
( - 1, -1/2)
5( - 1)^2
( - 1, 5)
-1/4( - 1)^2
( - 1, -1/4)
0
-1/2( 0)^2
( 0, 0)
5( 0)^2
( 0, 0)
-1/4( 0)^2
( 0, 0)
1
-1/2( 1)^2
( 1, -1/2)
5( 1)^2
( 1, 5)
-1/4( 1)^2
( 1, -1/4)
2
-1/2( 2)^2
( 2, -2)
5( 2)^2
( 2, 20)
-1/4( 2)^2
( 2, -1)
Now, let's draw the parabolas by plotting and connecting the obtained points.
Looking at the graphs, we can order the functions from widest to narrowest.
y=-1/4x^2, y=-1/2x^2, y=5x^2
