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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 http://mcgregormpm2d1.wikispaces.com/**

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

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

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

y = (x-1) 2-2 Space for work shown to students Calculate a with point (x,y) and vertex (h,k) substitute back in for a, h, k

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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)2 + 4 Homework Handout Pg. 185, Q # 6, 8, 13

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