10. Replace the x in the equation with each number in the input and the results will be the number in the output:
•input: -2 ---->output: -2
[tex]y = 2 - {( - 2)}^{2} \\ y = 2 - 4 \\ y = - 2[/tex]
•input: -1 ---> output: 1
[tex]y = 2 - {( - 1)}^{2} \\ y = 2 - 1\\ y = 1[/tex]
•input: 0 ---> output: 2
[tex]y = 2 - {( 0)}^{2} \\ y = 2 - 0 \\ y = 2[/tex]
•input: 1 ---> output: 1
[tex]y = 2 - {( 1)}^{2} \\ y = 2 - 1\\ y = 1[/tex]
•input: 2 ---> output: 4
[tex]y = 2 - {( 2)}^{2} \\ y = 2 - 4 \\ y = - 2[/tex]
now, you have the point you need to put in the graphic: (-2,-2); (-1,1); (0,2); (1,1); (2,-2)
once you make the graphic you can see it starts in y=-2 then goes up to y=2 and then goes down again to y=-2. It is a parabola and not a line, which is why it is a nonlinear equation
11. It is a linear equation because it follows the form: y=mx+b. In this case m= -1 and b= 1.
