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Bell Ringer 3/3/15

Bell Ringer 3/3/15. Factor x 2 + 6x + 9 x 2 - 10x + 25 x 2 + 12x + 36. Objective The student will be able to:. use the zero product property to solve equations. Zero Product Property. If a • b = 0 then a=0, b=0, or both a and b equal 0. 4 steps for solving a quadratic equation.

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Bell Ringer 3/3/15

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  1. Bell Ringer 3/3/15 • Factor • x2 + 6x + 9 • x2 - 10x + 25 • x2 + 12x + 36

  2. ObjectiveThe student will be able to: use the zero product property to solve equations

  3. Zero Product Property If a • b = 0 then a=0, b=0, or both a and b equal 0.

  4. 4 steps for solving a quadratic equation Set = 0 Factor Split/Solve Check • Set the equation equal to 0. • Factor the equation. • Set each part equal to 0 and solve. • Check your answer.

  5. 1. Solve (x + 3)(x - 5) = 0 Using the Zero Product Property, you know that either x + 3 = 0or x - 5 = 0 Solve each equation. x = -3 or x = 5 {-3, 5}

  6. 2. Solve (2a + 4)(a + 7) = 0 2a + 4 = 0 or a + 7 = 0 2a = -4 or a = -7 a = -2 or a = -7 {-2, -7}

  7. 3. Solve (3t + 5)(t - 3) = 0 3t + 5 = 0 or t - 3 = 0 3t = -5 or t = 3 t = -5/3 or t = 3 {-5/3, 3}

  8. 4. Solve x2 - 11x = 0 Set = 0 Factor Split/Solve Check GCF = x x(x - 11) = 0 x = 0 or x - 11 = 0 x = 0 or x = 11 {0, 11}

  9. Solve 1. -24a +144 = -a2 2. 4r3 – 16r = 0 3. 4m2 + 25 = 20m 4. x3 + 2x2 = 15x 5. a2 – 3a = 40

  10. Maria told this puzzle to her friends. “The product of four times my age and 45 less than three times my age is zero. How old am I?” Find Maria’s age. Let m = Maria’s age. 4m(3m - 45) = 0 4m = 0 or 3m - 45 = 0 m = 0 or 3m = 45 m = 0 or m = 15 0 is not reasonable so Maria is 15 years old!!

  11. Solving Quadratic Equations by Completing the Square

  12. Creating a Perfect Square Trinomial • In the following perfect square trinomial, the constant term is missing. X2 + 14x + ____ • Find the constant term by squaring half the coefficient of the linear term. • (14/2)2 X2 + 14x + 49

  13. Perfect Square Trinomials • Create perfect square trinomials. • x2 + 20x + ___ • x2 - 4x + ___ • x2 + 5x + ___ 100 4 25/4

  14. Solving Quadratic Equations by Completing the Square Solve the following equation by completing the square: Step 1: Move quadratic term, and linear term to left side of the equation

  15. Solving Quadratic Equations by Completing the Square Step 2: Find the term that completes the square on the left side of the equation.Add that term to both sides.

  16. Solving Quadratic Equations by Completing the Square Step 3: Factor the perfect square trinomial on the left side of the equation. Simplify the right side of the equation.

  17. Solving Quadratic Equations by Completing the Square Step 4: Take the square root of each side

  18. Solving Quadratic Equations by Completing the Square Step 5: Set up the two possibilities and solve

  19. Bell Work 3/13/14 Solving Quadratic Equations by Completing the Square.

  20. Bell Work 3/14/14

  21. Completing the Square-Example #2 Solve the following equation by completing the square: Step 1: Move quadratic term, and linear term to left side of the equation, the constant to the right side of the equation.

  22. Solving Quadratic Equations by Completing the Square Step 2: Find the term that completes the square on the left side of the equation.Add that term to both sides. The quadratic coefficient must be equal to 1 before you complete the square, so you must divide all terms by the quadratic coefficient first.

  23. Solving Quadratic Equations by Completing the Square Step 3: Factor the perfect square trinomial on the left side of the equation. Simplify the right side of the equation.

  24. Solving Quadratic Equations by Completing the Square Step 4: Take the square root of each side

  25. Solving Quadratic Equations by Completing the Square Try the following examples. Do your work on your paper and then check your answers.

  26. Bell Work 3/17/14 Solving Quadratic Equations by Completing the Square. 1) 6x 2 - 7x - 5 = 0 2) (1/2)x 2 - 4x + 8 = 0

  27. Quiz 3/18/14 1) Solving Quadratic Equations by Completing the Square. 6x 2 - 7x - 5 = 0 2) Solve the Rational Equation.

  28. Bell Work 3/31/14 • Write down the steps on how to solve Quadratic equations by completing the square. • Apply question 1 in solving the below quadratic Equations.

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