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Master Quadratic Equations Using Various Techniques

Practice solving quadratic equations via factoring, completing the square, and using the quadratic formula. Compare strategies and discuss complex solutions.

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Master Quadratic Equations Using Various Techniques

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  1. Warm up 9/09 Solve 1. x2 + 9x + 20 = 0 2. x2 - 7x = - 12 20 4 5 Turn and Talk 9 • What were the different strategies you used to solve each problems? • Is completing the square or factoring easier for you? Why? Shared

  2. Be seated before the bell rings Agenda: Warmup Go over hw Notes 5.6 DESK Warm-up (in your notes) homework • Ch 5 test tues 9/15

  3. Notebook 1 Table of content Page 12) 5.6 Quadratic Formula 7) 2.3 & 2.4 10) /5.3 Solve quadratics by factoring 11) 5.4 Solve Quadratics by Completing the Square 12) 5.6 Quadratic Formula 1

  4. 5.4: I can solve a quadratic equation by using square roots • 5.4: I can solve a quadratic equation by using the complete the square method. • 5.4: I can re-write a quadratic function in vertex form by completing the square. • 5.6: I can find the zeros/solutions of a quadratic equation using the quadratic formula Learning Targets

  5. 5.6 Quadratic Formula Use the quadratic formula to solve 5x2 + 6x = 2 ax2 + bx + c = 0 • Steps • Rearrange to standard form • Identify the a , b , c • Substitute into quad. formula • Solve/simplify 5x2 + 6x -2 = 0 a = 5 b= 6 c=-2

  6. Completing the Practice • Use the quadratic formula to solve the practice problem: x2 + 5x + 6 Turn and Talk: Compare your answer by factoring the quadratic and solving for x.

  7. The Discriminant b2 – 4ac 1. Positive  2 real solutions Example: x2 + 10x – 5 = 0 2. Zero  1 real solution Example: x2 + 4x + 4 = 0 3. Negative  No Real Solutions (2 complex solutions Example: 5x2 + 2x + 4 = 0 Turn and Talk: Why is √-80 not a real solution?

  8. Practice • Show and Explain how many solutions the following quadratic equations will have? 1. x2 + 8x + 16 = 0 2. x2 + 8x + 10 = 0 3. x2 + 5x + 7 = 0

  9. Complex Solutions i = √-1 i let’s us rewrite square roots without a negative number. Example: √-4 = Turn and Talk: Show and explain how to rewrite √-81 using i (√4)(√-1) = 2i

  10. More practice with rewriting

  11. An complex number has two parts Finding the complex zeros of Quadratic Function x2 –2x + 5 = 0

  12. Quadratic formula Practice • In pairs, Find the complex zeros of each. 1. x2 + 10x + 35 = 0 2. x2+ 4x + 13 = 0 3.x2 - 8x = -18

  13. Closer : Summarize: Write down one different thing each group member learn today into your notes. http://www.showme.com/sh/?h=eeY9fKi

  14. Additional Practice

  15. Quadratic formula Practice • In pairs, • Solve using the quadratic formula 1. x2+ 5x + 3 = 0 2. 3x2+ 10x + 7= 0 3.x2+ 11x = -6 4. x2 + 10x = 200

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