MBF 3CI ­ U4 ­ D5 ­ Applications of Quadratics ­ complete.notebook

1

December 18, 2014

Warm Up: Given the parabola y = -3(x + 4)2 -1, identify:

a = h = k =

MBF 3CI ­ U4 ­ D5 ­ Applications of Quadratics ­ complete.notebook

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December 18, 2014

Unit 4 ­ Quadratic Relations

Day 5:  y = a(x­h)2+k continued...

Today we will: 1. Use what we know about parabolas to answer real-life

problems

MBF 3CI ­ U4 ­ D5 ­ Applications of Quadratics ­ complete.notebook

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December 18, 2014

Applications of parabolas can be seen all around you if you look for them.• the arches of the bridge near Freeport hospital• the support wires of the San Francisco bridge• the path of a football, baseball, golf ball, ...• the relationship between revenue and number of items sold

Garden Bridge

Arched & Suspension Bridges

MBF 3CI ­ U4 ­ D5 ­ Applications of Quadratics ­ complete.notebook

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December 18, 2014

A parabola written in the form y = a(x - h)2 + k is said to be written in VERTEX form. Why?

A construction worker drops his wrench. Its fall is modelled by the relation h = -4.9t2 + 342 where h is the height above the ground, in metres, and t is the time after the wrench was dropped, in seconds.

What are the values of a, h and k?

Vertex

Direction of opening

Step pattern

Sketch this graph. Why do we only need one quadrant?

Example 1:

a) How far above the ground was the wrench when it was dropped?

b) How far has the wrench fallen after 5 seconds?

c) How far has the wrench fallen after 10 seconds? Does this make sense?

d) When will the wrench hit the ground?

MBF 3CI ­ U4 ­ D5 ­ Applications of Quadratics ­ complete.notebook

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December 18, 2014

A football player kicks a football held 0.5m above the ground. The football reaches a maximum height of 30m at a horizontal distance of 18m from the player.

b) At what horizontal distance from the player does the football hit the ground?

a) Determine a quadratic relation that models the path of the football.

Example 2:

Example 3:Sketch a parabola that has a width of 10 and a height of 7. Start your parabola at the vertical axis. Determine the equation of the parabola.

x

y

2 4 6-2-4-6

2

4

6

-2

-4

-6

8

8

-8

-8

10

10-10

MBF 3CI ­ U4 ­ D5 ­ Applications of Quadratics ­ complete.notebook

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December 18, 2014

Today's Practice Questions:p. 214 #5, 6, 7, 9

p. 222 #1 - 4

What is not finished in class is HOMEWORK!!!!

MBF 3CI ­ U4 ­ D5 ­ Applications of Quadratics ­ complete.notebook

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December 18, 2014