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Do Now 5/3/19

Learn how to solve quadratic equations by completing the square. Practice simplifying expressions and solving equations using the completing the square method.

johnmadison
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Do Now 5/3/19

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  1. Do Now 5/3/19 • Be ready to finish your quiz from yesterday. • In your Student Journal, review thenotesfromLesson 7.3 on page 216. Then complete the ODDS on page 217 & 218.

  2. Do Now 5/3/19 • Be ready to finish your quiz from yesterday. • In your notebook, simplify the followingexpressions. Do youremember the name of these expressions? (x + 5)² (2x – 4)²

  3. Essential QuestionHow can you use “Completing the Square” to solve a quadratic equation? • In your Student Journal, complete Explorations 1&2 on pages 291 & 292.

  4. Remember this??? Section 7.3 “Special Products of Polynomials” When squaring binomials, you can use the following patterns to help you. Binomial Square Pattern (addition) (a + b)² a² + 2ab + b² (a + b)(a + b) (x + 5)² x² + 10x + 25 (x + 5)(x + 5)

  5. Remember this??? Section 7.3 “Special Products of Polynomials” When squaring binomials, you can use the following patterns below to help you. Binomial Square Pattern (subtraction) (a – b)² a² – 2ab + b² (a – b)(a – b) (2x – 4)² 4x² – 16x + 16 (2x – 4)(2x – 4)

  6. Chapter 9 “Solving Quadratic Equations” • (9.1)Simplifying Radical Expression • (9.3)Solving Quadratic Equations Using Square Roots • (9.4) Solving Quadratic Equations by Completing the Square • (9.5) Solving Quadratic Equations Using the Quadratic Formula • (9.6) Solving Nonlinear Systems of Equations

  7. Learning Goal SWBAT solve quadratic equations Learning Target SWBAT solve quadratic equations by completing the square. 

  8. Section 9.4 “Solving Quadratic Equations by Completing the Square” • For an expression of the form x² + bx, you can add a constant c to the expression so thatx² + bx + c is a perfect square trinomial. This process is called x² + bx (1) Find one-half of b, the coefficient of x. (2) Square the result from Step 1. (3) Add the result from Step 2 to x2 + bx. 2 ( ) 2 b 2 2 ( ) x² + bx + b 2

  9. Complete the Square. Then factor the trinomial. x² + 8x (1) Find one-half of b, the coefficient of x. (2) Square the result from Step 1. (3) Add the result from Step 2 to x2 + bx. 2 2 ( ) 8 2 2 ( ) x² + 8x + 8 2 x² + 8x + (4)2 Factored trinomial (x + 4)(x + 4) x² + 8x + 16 (x + 4)2

  10. Complete the Square. Then Factor the Trinomial. On Your Own

  11. Solving Quadratic Equations by Completing the Square • The method of completing the square can be used to solve any quadratic equation, once the equation is in the form x² + bx = d. Complete the Square Add 64 to both sides of the equation Write the left side of the equation as a binomial (factor). Simplify right side of equation. Take the square root of both sides. Solve for x.

  12. Solve the quadratic equation by completing the square. Round your answer to the nearest hundredth if necessary.

  13. Solve the quadratic equation by completing the square. Round your answer to the nearest hundredth if necessary.

  14. Solve the quadratic equation by completing the square. Round your answer to the nearest hundredth if necessary. On Your Own

  15. ClassworkText p. 511, #6-32 evens

  16. HomeworkText p. 511, #6-32 evens

  17. Student Journal p. 294-295#1-18 all • ClassworkText p. 511, #6-32 evens • Text p. 511, #5-33 odds

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