Quadratics Solving equations Using “Completing the Square”

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Presentation transcript:

Quadratics Solving equations Using “Completing the Square”

Completing the square… ax² + bx + c = 0 Into the form p(x + r)² + s

Completing the square x² + 8x + 10 = 0x² + 6x + 24 = 0 (x + 4)² x² + 8x + 16 (x + 4)² - 6 = 0 (x + 3)² x² + 6x + 9 (x + 3)² + 15 = 0

Completing the Square ax² + bx + c = 0 Into the form p(x + r)² + s 2x² + 4x (x² + 2x) Complete the square: 2(x + 1)² 2(x² + 2x + 1) = 2x² + 4x + 2 2(x + 1)² + 13

Completing the Square 4x² + 16x – 2 = 0 4(x² + 4x) Complete the square: 4 (x + 2)² 4 (x + 2)² = 4( x² + 4x + 4) = 4x² + 16x (x + 2)² - 18 = 0

Completing the Square

Questions Complete the square for the expressions 1. x² + 4x 2. x² - 14x 3. x² - 6x 4. x² - 16x 5. x² + x 1. (x + 2)² - 2² 2. (x – 7)² - 7 ² 3. (x – 3)² - 3² 4. (x – 8)² - 8² 5. (x – ½)² - ½ ²