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Welcome to Pink Day!

Welcome to Pink Day!. Pick up notes and take out your homework. HW : Pg. 219 #13 - 33 odd Make notecards from U4L2. Updates: Unit 4 Quiz 1 (4.1-4.2) Monday. Agenda. Review HW Factoring Fun ! U4L2 Note-Card Practice Finish U4L2 Escape the Matrix! Cool-Down….

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Welcome to Pink Day!

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  1. Welcome to Pink Day! • Pick up notes and take out your homework. • HW: Pg. 219 #13-33odd Make notecards from U4L2. • Updates: • Unit 4 Quiz 1 (4.1-4.2) Monday

  2. Agenda • Review HW • Factoring Fun! • U4L2 • Note-Card Practice • Finish U4L2 • Escape the Matrix! • Cool-Down…

  3. Review HW Pg. 210 #15-35 odd, 39-45 (Do not graph) odd Questions? While you are doing the factoring activity, I am going to stamp it therefore, you are NOT turning it in!

  4. Learning Objective(s) By the end of this period you will be able to: • Solve quadratic equations using factoring, completing the square, quadratic formula, and graphing calculator. • How can we solve a quadratic equation? • Identify the number of complex roots for a polynomial equation. • How can we identify real and imaginary solutions algebraically?

  5. Factoring Fun! Now, some of you may be more uncomfortable with factoring so lets take the time to practice! • Factor each side of the square and find its match on another square. • You must separate the squares amongst your table-mates so that everyone in your table is doing the same amount of work. • I need to see everyone participating. If you are not, then you will lose participation points. Do the work on your whiteboard. • You should get a 4x4 squarein the end.

  6. Quadratic Equations (4.2) • Solve quadratic equations using factoring, completing the square, quadratic formula, and graphing calculator. • How can we solve a quadratic equation? There are four methods for solving a quadratic equation: • Factoring • Completing the Square • Quadratic Formula • Graphing Calculator

  7. Quadratic Equations (4.2) • Factoring • Factor into two sets of parentheses. • Example: Solve 2x2 + x – 6 = 0 (x+2)(2x-3)=0 x = -2 and x = 3/2 • You cannot always factor! Highlight: You cannot always factor!

  8. Quadratic Equations (4.2) (2) Completing the Square • Steps: • Make the leading coefficient 1. • Put all variables on one side of the equal sign and constants on the other side of the equal sign. • Add (b/2)2 to both sides of the equation. • Factor the variable side into a perfect square and simplify the constant side. • Solve for x. • This method works for ALL quadratic equations. (HIGHLIGHT) Discuss in your tables. Will this method work for ALL quadratic equations?

  9. Quadratic Equations (4.2)

  10. Whiteboards! Solve by completing the square. 2g2+ 11g -21 = 0

  11. Quadratic Equations (4.2) (3) Quadratic Formula • The quadratic formula: Where a ≠ 0. • This method works for ALL quadratic equations. ( Highlight) Discuss in your tables. Will this method work for ALL quadratic equations? Let’s listen to a song!

  12. Quadratic Equations (4.2) Conjugates • Imaginary roots of polynomial equations with real coefficients always occur in conjugate pairs, a + bi and a– bi where b ≠ 0. • Like we saw in ( c ) and ( d)

  13. Whiteboards! Solve the quadratic equation using the quadratic formula. 36d2 – 84d + 49 = 0

  14. Note-Card Practice! Seat #1/2 are partners and #3/4 are partners! Choose one person to go 1st. The 1st person will use there notecards and show the 2nd person a word and the 2nd person is to say the definition. You will go through the stack. Switch. Now, 1st person will define the words as the 2nd person shows them the vocabulary words. You will have 4 minutes of note-card practice.

  15. Quadratic Equations (4.2) • Identify the number of complex roots for a polynomial equation. • How can we identify real and imaginary solutions algebraically? Discriminant • b2– 4ac (the expression under the radical in quadratic formula) • If b2 – 4ac > 0 • If b2 – 4ac = 0 • If b2 – 4ac < 0 Two real roots One real root No real root

  16. Quadratic Equations (4.2)

  17. Quadratic Equations (4.2) • Solve quadratic equations using factoring, completing the square, quadratic formula, and graphing calculator. • How can we solve a quadratic equation? (4) Graphing Calculator • Steps: • Type in y = 2x2 + 11x – 21 • Zoom 6 or Zoomfit • 2nd trace • #2 Zero • Left Bound (go to the left of the root) Enter • Right Bound (go to the right of the root) Enter • Guess (go to the root) Enter • Can only be used when we have no imaginary solutions.

  18. Quadratic Equations (4.2)

  19. Escape the Matrix • Please change the address ( 2,3) in the matrix to the following: Remember matrices? 4x2 +6x – 4 = 0

  20. Escape the Matrix • Put the paper inside your whiteboard. • You are going to solve these quadratic equations in ANY way that you wish! • You are going to look for the solutions and then shade the box! Your goal is to Escape the Matrix! • Good Luck  Raise your hand when you think you figured out the correct path!

  21. Cool-Down… Exit Ticket: Put everything away except for a pencil and eraser. Split the paper that I give you among your table group. Write your name and table # on the top right. Try your best; this is for me to see how much you understand the material. Solve the polynomial by completing the square or using the quadratic formula.

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