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Graphing Parabolas MPM 2D1

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Agenda Warm up Properties of Parabolas Parabolas in our Lives Practical Applications TOC

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Warm up Class Website Untie the knot

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Properties of Parabolas

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Matching Activity You will be given a word, or a property of the parabola shown You are responsible for finding the person with the paper that is the match to yours Sit with your partner when you found them

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Matching Activity (-2, -7) (0, 0.64) a = 1

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Graph to Equation (1, -2) (2, -1)

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Graph to Equation h = 1, k = -2 x = 2, y = -1 y = a(x-h )2 +k -1 = a(2-1) = a(1) 2 1 = a Equation y = (x-1) 2 -2

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Parabolas in our Lives Top edge of a spoon Motion of a swing Face shape Roller coaster Arrow projectory A bow Arch of a bridge Horseshoe Top of a mushroom Shoe front

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Practical Applications The flight path of a firework is modelled by the relation h = -5(t-5) , where h is the height, in metres, of the firework above the ground and t is the time, in seconds, since the firework was fired.

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Practical Applications A) what is the maximum height reached by the firework? How many seconds after it was fired does the firework reach this height? Looking for the vertex point Maximum height y coordinate (k) Seconds after fired x coordinate (h) k = 127 h = 5

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Practical Applications B) How high was the firework above the ground when it was fired? Looking for the y-intercept (firework was fired at t=0) Sub in t=0 h = -5(0-5) h = -5(-5) h = -5(25)+127 h = h = 2 m

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TOC State the vertex and axis of symmetry for the following equation: y = (x+2) Homework Handout Pg. 185, Q # 6, 8, 13

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