help with quadratic equation?

Question

x y
0 2
14 287
28 434
42 445
56 318
70 54

write an equation that best fits the scatter plot. (quadratic equation)

Answer 1

y = ax^2 + bx + c
2 = a(0)^2 + (0)x + c
c = 2

y = ax^2 + bx + 2

54 = a(70)^2 + b(70) + 2
54 = a(4900) + b(70) + 2
4900a + 70b = 52

445 = a(42)^2 + b(42) + 2
445 = a(1764) + b(42) + 2
1764a + 42b = 443
a = (443 - 42b) / 1764

4900((443 - 42b) / 1764) + 70b = 52
1230.555 - 116.666b + 70b = 52
1230.555 - 46.666b = 52
-46.666b = -1178.555
b = 25.255

a = (443 - 42(25.255)) / 1764
a = -0.35

y = (-0.35)x^2 + (25.255)x + 2

Answer 2

the curve is a polynomial of the type ax^2+bx+c=0
by substituting the values we can evaluate a,b and c