Find Equation of Parabola Passing Through Three Points

Find the equation of a parabola \( y = ax^2 + bx + c \) that passes through three given points. Generate random points, see detailed step-by-step solutions using Cramer's Rule, and visualize the parabola.

📐 Parabola Through Three Points

Find \( y = ax^2 + bx + c \) passing through points A, B, C

Points: A(0, 1), B(1, 0), C(-1, 0)
Find the equation of the parabola \( y = ax^2 + bx + c \) through these points.

📖 Step-by-Step Solution

STEP 1: Check if points are collinear
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STEP 2: Write the system of equations
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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 and write the parabola equation
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📊 Graphical Visualization
Parabola: Green | Points A, B, C: Red

Adjust axis scale to see the parabola and points clearly.