Quadratic Equation by Completing Sq.ppt
- 1. Do Now Factor the expression. 1. x2 + 18x + 81 1. x2 - 22x + 121
- 2. Completing the Square OBJECTIVE: SOLVE QUADRATIC EQUATIONS BY COMPLETING THE SQUARE
- 3. Completing the Square Find the value of c that makes x2 - 6x + c a perfect square trinomial. Then write the expression as the square of a binomial. To find the value of c, use the “b” value (ax2 +bx+c): 1. Find half the coefficient of x. 2. Square the result of Step 1. 3. Replace c with the result of Step 2. Answer: when when c c = 9, = 9, x x2 2 – 6 – 6x x + 9 = ( + 9 = (x x – 3) – 3)2 2 x x2 2 – 6 – 6x x + 9 + 9 (– 3) (– 3)2 2 = = ½ (– 6) ½ (– 6) = =
- 4. Example: Completing the Square Find the value of c that makes x2 - 12x + c a perfect square trinomial. Then write the expression as the square of a binomial. To find the value of c, use the “b” value (ax2 +bx+c): 1. Find half the coefficient of x. 2. Square the result of Step 1. 3. Replace c with the result of Step 2. Answer:
- 5. Practice Find the value of c that makes the expression a perfect square trinomial. Then write the expression as the square of a binomial. 3. x2 - 10x + c 4. x2 + 18x + c
- 7. Example
- 8. Solve the equation by completing the square. 1. x2 + 2x – 3 = 0 2. x2 - 6x + 16 = 0
- 9. Solve the equation by completing the square. 3. x2 - 8x - 20 = 0 4. x2 + 4x - 15 = 21
- 10. Solve the equation by completing the square. 5. x2 - 2x - 2 = 0 6. x2 + 6x + 3 = 0