Solving quadratic equations

Solving Quadratic Equations Methods: Factoring Square Roots Completing the Square

Solutions of a Quadratic Equation ,[object Object],[object Object],X = 3? X = 5? X = 0? X = -1? 3 ² - 4(3) = 5? 5 ²-4(5)=5? 9 – 12 = 5? 25-20=5? -3  5 5 = 5 3 is NOT 5 IS a solution a solution

Review: Factor a Quadratic Expression ,[object Object],[object Object],[object Object],[object Object]

Factoring Practice ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],1. (x+9)(x-8) 2. (5-6x)(5+6x) 3. 4x(x+1)(x-1) 4. 7x ²y(3x+4y) 5. (2x-1)(x-2)

Solve by Factoring ,[object Object],[object Object],[object Object],Example: 2x ² = 4x 2x² - 4x = 0 2x (x - 2) = 0 2x = 0 OR x – 2 = 0 X = 0 OR x = 2 Solutions/roots: {0, 2}

Solve by Factoring Examples ,[object Object],[object Object]

Solve by Factoring Application Example #1 ,[object Object],[object Object],[object Object],[object Object]

Solve by Factoring Application Example #2 ,[object Object],[object Object],[object Object],[object Object]

Write a Quadratic Equation Given Roots ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],This is the quadratic equation with roots {-2, 6}

Solve Quadratic by Square Roots ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Solve Quadratics by Square Roots Examples ,[object Object],[object Object]

Solve Quadratic by Completing the Square ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Solve Quadratic by Completing the Square Examples ,[object Object],[object Object]

Solving quadratic equations

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Solving quadratic equations