Question 1060415

I need your assistance to help find the quadratic function that models the data below please.

xI  -3      -2      -1    0   1     2      3        4       5           6           7           8           9
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yI   54     26     -8     0   2   14     36     68     110       162       224      296         378


I need help with this please.  When I look at this all i'm seeing is a chart I don't know how I would work this out
<pre>The EASIEST way to do this is to take the 3 EASIEST points to get the quadratic function. These points are: (0, 0), (- 1, - 8), and (1, 2)				
Quadratic function: {{{matrix(1,3, f(x) = ax^2 + bx + c, or, ax^2 + bx + c = 0)}}}
(0, 0)
{{{ax^2 + bx + c = y}}}
{{{a(0)^2 + b(0) + c = 0}}} --------- Substituting point (0, 0) for (x, y)				
0 + 0 + c = 0____{{{highlight(c = 0)}}} ------ eq (i)

(- 1, - 8)
{{{ax^2 + bx + c = y}}}
{{{a(- 1)^2 + b(- 1) + 0 = - 8}}} ---- Substituting point (- 1, - 8) for (x, y), and 0 for c
a - b = - 8 ----- eq (ii)

(1, 2) 	
{{{ax^2 + bx + c = y}}}
{{{a(1)^2 + b(1) + 0 = 2}}} --------- Substituting point (1, 2) for (x, y), and 0 for c				
a + b = 2 ------- eq (iii)
2a = - 6 -------- Adding eqs (ii) & (iii)
{{{highlight(matrix(1,3, a = (- 6)/2, or, - 3))}}} 

- 3 + b = 2 ------- Substituting - 3 for a in eq (iii)
{{{highlight(b = 5)}}}

{{{f(x) = ax^2 + bx + c}}}	
{{{f(x) = - 3x^2 + 5x + 0}}} ------- Substituting - 3 for a, 5 for b, and 0 for c
Quadratic function: {{{highlight(highlight_green(highlight(f(x) = - 3x^2 + 5x)))}}}