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Using a 3 Variable System to find a Quadratic Equation Writing a Contextual 3 Variable System Suppose the graph of a quadratic function passes through the points (1,0), (2,5), and (3,12). Algebraically find the quadratic equation. 1. Use the Standard Quadratic Form: y ax bx c 2 x y 0 a 1 b 1 c 2 2. Substitute each Point into the Equation: 5 a 2 2 b 2 c 12 a 3 b 3 c 2 0 abc 3. Simplify the Equations: 5 4a 2b c 12 9a 3b c Solving a Contextual 3 Variable System Solve the system: 1 0 a b c 1 Eliminate 2 5 4a 2b c the “c” first! 3 12 9a 3b c 1. Use Elimination to write a 2-Variable System 1 2. Solve the new system 10 6a 2b + 12 8a 2b 2 2a 1 a 0 a b c 0 a b c 2 3 5 4 a 2 b c + +12 9a 3b c 5 3a b 12 8a 2b 1 5 3a b 2 12 8a 2b 5 3 1 b 5 3b 2b 3. Solve for the 3rd Variable 0 1 2 c 0 3 c 3 c 4. Subsititue into the Standard Form: y x 2x 3 2