Given:-
A set of data.
To find the required equation.
So from the given equation, the equation which suits is,
[tex]y=2x^2-2[/tex]So now we prove it by substituting the values from the table.
When x=-2 we get the value as,
[tex]\begin{gathered} y=2x^2-2 \\ y=2(-2)^2-2 \\ y=2\times4-2 \\ y=8-2 \\ y=6 \end{gathered}[/tex]So the value of y is 6.
When x=-1. we get,
[tex]\begin{gathered} y=2x^2-2 \\ y=2(-1)^2-2 \\ y=2\times1-2 \\ y=2-2 \\ y=0 \end{gathered}[/tex]So the value of y is 0.
When x=0. we get,
[tex]\begin{gathered} y=2x^2-2 \\ y=2(0)-2 \\ y=-2 \end{gathered}[/tex]So the value of y is -2.
When x=1. we get,
[tex]\begin{gathered} y=2x^2-2 \\ y=2(1)-2 \\ y=2-2 \\ y=0 \end{gathered}[/tex]So the value of y is 0.
When x=2. we get,
[tex]\begin{gathered} y=2x^2-2 \\ y=2(2)^2-2 \\ y=2\times4-2 \\ y=8-2 \\ y=6 \end{gathered}[/tex]So the value of y is 6.
When x=3. we get,
[tex]\begin{gathered} y=2x^2-2 \\ y=2(3)^2-2 \\ y=2\times9-2 \\ y=18-2 \\ y=16 \end{gathered}[/tex]So the value of y is 16.
When x=4. we get,
[tex]\begin{gathered} y=2x^2-2 \\ y=2(4)^2-2 \\ y=2\times16-2 \\ y=32-2 \\ y=30 \end{gathered}[/tex]So the value of y is 30.
So from this we can conclude that the correct equation is,
[tex]y=2x^2-2[/tex]