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Find an equation of the cubic function whose graph passes through (3, -4), (-1, 2), (0, 0), and (7, 5).

 Feb 26, 2021
 #1
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Let the cubic be in the form f(x) = ax^3 + bx^2 + cx + d.

 

We have four points and four variables, so plug them in:

 

 

(3, -4) ==> 27a + 9b + 3c + d = -4

(-1, 2) ==> a - b + c - d = 2

(0, 0) ==> d = 0

(7, 5) ==> 343a + 49b + 7c + d = 5

 

Use WolframAlpha or a similar program to solve for a, b, c, and d.

 Feb 26, 2021

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