The Windsor-Detroit International Freedom Festival hosts one of the largest firework displays in the world.

mathematics

Description

1)      Find the y-intercept for each relation (simply set x to 0)


a)      y = -15x2 + 25x – 7

b)      y = 20(x – 12)2 + 15

c)      y = 10x2 + 8x – 3

d)     y = -0.1x2 - -.4x – 18

e)      y  = 0.45x2 – 0.17x + 20

f)       y = -0.5(x + 1.5)2  + 4.5

g)      y = 0.2(x – 3.4)2  + 1

h)      y = -3(x + 2)2 + 9


2)      For each parabola identify the :


x and y intercepts


maximum or minium value (of y)


3)      The Windsor-Detroit International Freedom Festival hosts one of the largest firework displays in the world. The path of a particular firework rocket is modelled by the relation h = -4.9(t – 2)2 + 169.6, where h is the height of the rocket above the water, in meters, and t is the time in seconds.

a)      How long will it take the rocket to reach is’t maximum height and what is that height?

 

 

 

 

 

 

 

b)      A firework rocket will stay lit for an average of five seconds. How high will the rocket be five seconds following its launch?

 

 

 

 

 

 

 

4)      The shape of satellite dish is parabolic. This dish is 5 cm deep and 40 cm wide. Write a relation of the form y = a(x-h)2 + k that models the shape of this dish. It’s up to you to decide where the origin is.


 

(Hint: You have the vertex, and you have a second point,

 

 

 

 

 

 

 

 

 

 

 

 

 

 



5)      Automobile manufactures have invented some unique car designes to help drivers cope with rising fuel costs. The Smart Car Fortwo is a very small, fuel-efficient vehicle. The distance it travels when accelerating from rest can be modelled by the relation d = 1.4t2. The Tesla Roadster is an electric car with a top sped of over 200 km / h. The distance it travels when accelerating from rest can be modelled by the relation d = 6.9t2. In both cases, d is distance in meters, t is time in seconds.

 

 

a)      Complete the following table:

 

Time, t

(Seconds)

Distand, dS of Smart Car

(Meters)

Distand, dT of Tesla Roadster

(Meters)

0

 

 

1

 

 

2

 

 

3

 

 

4

 

 

5

 

 

 

 

b)      Graph the data

 

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