Answer:
The given function is a nonlinear function because the degree of the function is 2 and we get same value of y for more than one values of x.
Step-by-step explanation:
The given function is
![y=2x^2-5](https://tex.z-dn.net/?f=y%3D2x%5E2-5)
To find the points which lie on the function, put difference values of x in the given function and find the values of y.
Put x= -2
![y=2(-2)^2-5=2(4)-5=8-5=3](https://tex.z-dn.net/?f=y%3D2%28-2%29%5E2-5%3D2%284%29-5%3D8-5%3D3)
Put x= -1
![y=2(-1)^2-5=2(1)-5=2-5=-3](https://tex.z-dn.net/?f=y%3D2%28-1%29%5E2-5%3D2%281%29-5%3D2-5%3D-3)
Put x= 0
![y=2(0)^2-5=2(0)-5=-5=-5](https://tex.z-dn.net/?f=y%3D2%280%29%5E2-5%3D2%280%29-5%3D-5%3D-5)
Put x=1
![y=2(1)^2-5=2(1)-5=2-5=-3](https://tex.z-dn.net/?f=y%3D2%281%29%5E2-5%3D2%281%29-5%3D2-5%3D-3)
Put x= 2
![y=2(2)^2-5=2(4)-5=8-5=3](https://tex.z-dn.net/?f=y%3D2%282%29%5E2-5%3D2%284%29-5%3D8-5%3D3)
The table of values is shown below.
Plot these points on a coordinate plane and connect them by a free hand curve.
The given function is a nonlinear function because the degree of the function is 2 and we get same value of y for more than one values of x.
The graph of function is shown below.
I have attached the graph. Your axis is x=-4 and the vertex is (-4,-30)
Hope that helps