Question

Find a polynomial of the form $f(x) = ax^3 + bx^2 + cx + d$ such that $f(0) = -3$, $f(2) = 2$, $f(4) = 2$, and $f(5) = 1$. Answer: $f(x) = \frac{7}{120}x^3 - \frac{39}{40}x^2 + \frac{253}{60}x - 3$

          Find a polynomial of the form
$f(x) = ax^3 + bx^2 + cx + d$
such that $f(0) = -3$, $f(2) = 2$, $f(4) = 2$, and $f(5) = 1$.
Answer: $f(x) = \frac{7}{120}x^3 - \frac{39}{40}x^2 + \frac{253}{60}x - 3$

Find a polynomial of the form
f(x) = ax^3 + bx^2 + cx + d
such that f(0) = -3, f(2) = 2, f(4) = 2, and f(5) = 1.
Answer: f(x) = (7)/(120)x^3 - (39)/(40)x^2 + (253)/(60)x - 3

Added by Stephanie H.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Ernest Castorena

06/11/2020

Step 1

Step 1: Start by setting up the system of equations based on the given information: f(0) = -3: 0 = d f(2) = 2: 2a(2)^3 + 2b(2)^2 + 2c + d = 2 f(4) = 2: 2a(4)^3 + 2b(4)^2 + 4c + d = 2 f(5) = 1: 2a(5)^3 + 2b(5)^2 + 5c + d = 1 Show more…

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Find a polynomial of the form f(x)=ax^(3)+bx^(2)+cx+d such that f(0)=-3,f(2)=2,f(4)=2, and f(5)=1. Answer: f(x)= Find a polynomial of the form f(x)=ax3+bx2+cx+d such that f(0= -3, f(2)=2,f(4) =2,and f(5)=1 Answer: f()= 7/120*x^3-39/40*^2+253/60*-3