We want to order the given quadratic functions from widest to narrowest graph.
f(x)=-2x^2, f(x)=-2/3x^2, and f(x)=-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.
f(x)=-2x^2
f(x)=-2/3x^2
f(x)=-4x^2
x
-2x^2
(x,y)
-2/3x^2
(x,y)
-4x^2
(x,y)
- 2
-2( - 2)^2
( - 2, -8)
-2/3( - 2)^2
( - 2, -8/3)
-4( - 2)^2
( - 2, -16)
- 1
-2( - 1)^2
( - 1, -2)
- 2/3( - 1)^2
( - 1, - 2/3)
-4( - 1)^2
( - 1, -4)
0
-2( 0)^2
( 0, 0)
- 2/3( 0)^2
( 0, 0)
-4( 0)^2
( 0, 0)
1
-2( 1)^2
( 1, -2)
- 2/3( 1)^2
( 1, - 2/3)
-4( 1)^2
( 1, -4)
2
-2( 2)^2
( 2, - 8)
- 2/3( 2)^2
( 2, - 8/3)
-4( 2)^2
( 2, -16)
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.
f(x)=-2/3x^2, f(x)=- 2x^2, f(x)=-4x^2
