find the equation to cubic function P, that has P(x) intercept equal to 5 with P(1)=7 and P(2)=14

Question

a cubic function P, has P(x) intercept equal to 5. Also P(1)=7 and P(2)=14. Find the particular equation for P(x)

Answer 1

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.