Question

I need helping answering 15. I need to create a table and graph the function.

Answer 1

ANSWER and EXPLANATION

We want to order the functions from widest to narrowest:

`\begin{gathered} y=3x^2 \\ y=2x^2 \\ y=4x^2 \end{gathered}`

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:

`\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}`

Hence, its table is:

For the second function:

`\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}`

Hence, its table is:

For the third function:

`\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}`

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:

`y=2x^2;y=3x^2;y=4x^2`