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5.8 Quadratic Formula

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5.8 Quadratic Formula

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    1. 5.8 – Quadratic Formula

    2. Ready to SING? X = -b +

    3. Quadratic Formula Great for solving ax˛ + bx + c = 0

    4. Let’s try one out Use the quadratic formula to solve for x 3x2 – x - 6 a = 3, b = -1, c = -6

    5. Let’s try it out Use the quadratic formula to solve for x 3x2 -x -6

    6. Let’s try one with a complex root 2x2 + 2x + 5

    7. Let’s try one with a complex root 2x2 + 2x + 5

    8. Let’s go back to our equation X = -b +

    9. Test the discrininant If b2- 4ac > 0 If b2- 4ac < 0 If b2- 4ac = 0

    10. Sample Problem Given the equation x2 + 3x – 4, how many solutions will the graph have? Real or imaginary?

    11. WORD PROBLEM #1 A pool measuring 12 meters by 16 meters is to have a pedestrian pathway installed all around it, increasing the total area to 247 square meters. What will be the width of the pathway?

    12. A pool measuring 12 meters by 16 meters is to have a pedestrian pathway installed all around it, increasing the total area to 285 square meters. What will be the width of the pathway? SET UP We know length x width = area Therefore (2x+16) (2x + 12) = 285

    13. WORD PROBLEM # 2 A rocket is launched directly upward at 64 feet per second (ft/s) from a platform 80 feet high. What will be the object's maximum height? When will it attain this height? Use the formula, where and

    14. A rocket is launched directly upward at 64 feet per second (ft/s) from a platform 80 feet high. What will be the object's maximum height? When will it attain this height? Use the formula, where and ANSWER QUESTION What will be the object's maximum height? Max height happens at vertex. VERTEX = ( -b / 2a , f(-b / 2a) ) Remember a = -16 , b = 64, c = 80 So – b /2a = -64/2(-16) = 2 Since t= time, it will take 2 seconds to reach the max height To find the actual max height, plug in t = 2. -16(2)˛ + 64(2) + 80 = 144 So the object will reach the max height of 144 feet at 2 seconds after launch SET UP We know h = -16t˛ + vot + ho and that Vo = 64 and ho = 80 therefore h = -16t˛ + 64t + 80

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