Find an equation to describe the following data, (4, 3), (6, $1.50), (8, 6)

Answer 1

well one way is a parabola

write a parabola that goes through
(4,1) (6,1.5) and (8,6)
first
(4,3) (6,0) and (8,0)
Y1 = 3(x-6)(x-8) /(4-6)(4-8)
= 3(x^2 -14 x + 48)/ 8
second
(4,0)(6,1.5)(8,0)
Y2 = 1.5 (x-4)(x-8)/(6-4)(6-8)
= -(1.5 x^2 -18 x +48)/4
third
Y3 = 6(x-4)(x-6)/(8-4)(8-6)
= (6 x^2 -60 x +144)/8
The parabola Y1+Y2+Y3 goes through the three points