ANSWER and EXPLANATION
We want to order the functions from widest to narrowest:
[tex]\begin{gathered} y=3x^2 \\ y=2x^2 \\ y=4x^2 \end{gathered}[/tex]
To do this, we have to plot the graphs of the functions by using a table of values.
Let us find the values of the functions for values of x = -2, 0, 2
For the first function:
[tex]\begin{gathered} y=3x^2 \\ \Rightarrow x=-2: \\ y=3(-2)^2=3*4 \\ y=12 \\ \Rightarrow x=0: \\ y=3(0)^2=3*0 \\ y=0 \\ \Rightarrow x=2: \\ y=3(2)^2=3*4 \\ y=12 \end{gathered}[/tex]
Hence, its table is:
For the second function:
[tex]\begin{gathered} y=2x^2 \\ \Rightarrow x=-2: \\ y=2(-2)^2=2*4 \\ y=8 \\ \Rightarrow x=0: \\ y=2(0)^2=2*0 \\ y=0 \\ \Rightarrow x=2: \\ y=2(2)^2=2*4 \\ y=8 \end{gathered}[/tex]
Hence, its table is:
For the third function:
[tex]\begin{gathered} y=4x^2 \\ \Rightarrow x=-2: \\ y=4\left(-2\right)^2=4*4 \\ y=16 \\ \Rightarrow x=0: \\ y=4(0)^2=4*0 \\ y=0 \\ \Rightarrow x=2: \\ y=4(2)^2=4*4 \\ y=16 \end{gathered}[/tex]
Hence, its table is:
Now, let us plot the graphs of the functions:
Therefore, from the graph, we see that the order of the functions from widest to narrowest is:
[tex]y=2x^2;y=3x^2;y=4x^2[/tex]
