Which of the following is a nonlinear function?

a.
input
1
2
3
4
5
output
4
12
20
28
36

b.
input
1
2
3
4
5
output
4
16
64
256
1,024

c.
input
1
2
3
4
5
output
4
10
16
22
28

d.
input
1
2
3
4
5
output
4
8
12
16
20

if the eqn of the parabola is f(x) = (x-4)(x+2), we need to mult. this out to find the coordinates of the vertex.

then f(x) = x^2 + 2x - 4x - 8, and f(x) = x^2 - 2x - 8.

one way in which you can find the vertex is to calculate x = -b / (2a).   here, that comes to

        )

x = = 1.   f(1) = 1^2 - 2(1) - 8 = - 9.   vertex is at (1, -9).

        2(1) 

find another point on the curve:   let x=0, for which y=-8.   then (0, -8) is on the curve.   plot the vertex and this point and draw a smooth parabola thru both.

hope this