What rule will represent the function, (0,0), (1,1), (2,4), (3,9), (4,16)

a(n) = (n-1)^2

Step-by-step explanation:

Notice that each of the y-values {0, 1, 4, 9, 16, ... } is a perfect square.  Thus,

the rule is a(n) = (n-1)^2.

Check:  if n = 0, is (n-1)^2 = 0?  yes

             if n = 3, is (3-1)^2 = 4?  yes

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

- 70

this is the answer for you hope it