Find a Cubic Polynomial Passing Through Four Points

Find the cubic polynomial \( P(x) = ax^3 + bx^2 + cx + d \) that passes through four given points. Generate random points, see detailed steps using Cramer's Rule with 4×4 determinants, and visualize the polynomial.

📐 Cubic Polynomial Through Four Points

Find \( P(x) = ax^3 + bx^2 + cx + d \) passing through points A, B, C, D

Points: A(0, 1), B(1, 0), C(2, 1), D(3, 6)
Find the cubic polynomial \( P(x) = ax^3 + bx^2 + cx + d \) through these points.

📖 Step-by-Step Solution

STEP 1: Write the general form of the cubic polynomial
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STEP 2: Write the system of equations from the four points
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STEP 3: Set up determinants for Cramer's Rule
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STEP 4: Evaluate the determinants
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STEP 5: Calculate a, b, c, d and write the polynomial
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📊 Graphical Visualization
Polynomial: Green | Points A, B, C, D: Red

Adjust axis scale to see the polynomial and points clearly.