Let P(x)=a₀+a₁x+a₂x²+a₃x³ where a₀,...a₃ are constant coefficients.
P(0)=5 (intercept), so a₀=5. Let a₃=1.
P(x)=5+a₁x+a₂x²+x³.
P(1)=7=5+a₁+a₂+1, a₁+a₂=1, a₂=1-a₁
P(2)=14=5+2a₁+4a₂+8,
2a₁+4a₂=1=2a₁+4-4a, 2a₁=3, a₁=3/2, a₂=1-3/2=-½.
P(x)=x³-x²/2+3x/2+5.