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**Solving realistic problems using quadratics**

The trick is selecting the BEST (quickest, easiest, laziest) way to solve!

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**EX 1 This parabola models the height of a ball tossed into the air**

EX 1 This parabola models the height of a ball tossed into the air. Determine its equation.

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**A) Determine an equation to model the flight path**

EX 2 At a fireworks display, a firework is launched from a height of 2 m above ground and reaches a maximum height of 40 m, 10 m away along the ground from where it was launched. A) Determine an equation to model the flight path

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EX 2 At a fireworks display, a firework is launched from a height of 2 m above ground and reaches a maximum height of 40 m, 10 m away along the ground from where it was launched. B) After the firework reaches its max height, it continues on its path for another 1 m in terms of horizontal distance before it explodes. What is its height when it explodes?

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EX 2 At a fireworks display, a firework is launched from a height of 2 m above ground and reaches a maximum height of 40 m, 10 m away along the ground from where it was launched. C) In the last question, we found the firework is at a height of _______ where the horizontal distance from the launch point is ______. At what other place (horizontally) is the firework at the same vertical height?

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**EX 3 The Dufferin Gate is a parabolic arch that is approximately 20 m tall and 22 m wide.**

Determine an equation to model the arch.

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EX 4 p. 278 #18: Many suspension bridges hang from cables that are supported by two towers. The shape of the hanging cables is very close to a parabola. A typical suspension bridge has large cables that are supported by two towers that are 20 m high and 80 m apart. The bridge surface is suspended from the large cables by many smaller vertical cables. The shortest vertical cable is 4 m long. A) Using the bridge surface as the x-axis, find an equation to represent the parabolic shape of the large cables

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**B) How long are the vertical cables that are 25 m from each tower?**

EX 4 p. 278 #18: Many suspension bridges hang from cables that are supported by two towers. The shape of the hanging cables is very close to a parabola. A typical suspension bridge has large cables that are supported by two towers that are 20 m high and 80 m apart. The bridge surface is suspended from the large cables by many smaller vertical cables. The shortest vertical cable is 4 m long. B) How long are the vertical cables that are 25 m from each tower?

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