sec 3 - university of minnesotahankx003/fall2012/lectures/ch3sec4.pdf · quadratic models sec 3.4....
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Sec 3.4
Quadratic Models
Math 1051 - Precalculus I
Quadratic Models Sec 3.4
Sec 3.4 Quadratic Models
Find the vertex and axis of symmetry of
f (x) = −3x2 + 6x + 9
Ans: Vertex (1,12), Axis of Symmetry x = 1
Quadratic Models Sec 3.4
Sec 3.4 Quadratic Models
Find the vertex and axis of symmetry of
f (x) = −3x2 + 6x + 9
Ans: Vertex (1,12), Axis of Symmetry x = 1
Quadratic Models Sec 3.4
Today...
More word problems!
Quadratic Models Sec 3.4
Today...
More word problems!
Quadratic Models Sec 3.4
The price p (dollars) and the quantity x sold of a certain productobey the demand equation
p(x) = −13
x + 100
for 0 ≤ x ≤ 300.
Express the revenue R as a function of x
Quadratic Models Sec 3.4
R(x) = −13
x2 + 100x
-100 100 200 300
2000
4000
6000
8000
Quadratic Models Sec 3.4
You own a club which has 400 members who pay $500 permonth in membership dues. You would like to make moremoney by lowering the price of membership. You make thefollowing observation:
For every $1 you lower the membership 2 extra people will join.What is the “optimal” price?
Quadratic Models Sec 3.4
You own a club which has 400 members who pay $500 permonth in membership dues. You would like to make moremoney by lowering the price of membership. You make thefollowing observation:
For every $1 you lower the membership 2 extra people will join.What is the “optimal” price?
Quadratic Models Sec 3.4
R(p) = −2p2 + 1400p
200 400 600 800
50 000
100 000
150 000
200 000
250 000
Quadratic Models Sec 3.4
A farmer has 2000 meters of fencing. He wants to enclose arectangular plot of land to grow corn in.
Inside he also wants to enclose a circular pond with the fence,with the diameter of the pond half the length of the shorter sideof the field.
What should the length and width of the rectangle be tomaximize the area for corn?
Quadratic Models Sec 3.4
A farmer has 2000 meters of fencing. He wants to enclose arectangular plot of land to grow corn in.
Inside he also wants to enclose a circular pond with the fence,with the diameter of the pond half the length of the shorter sideof the field.
What should the length and width of the rectangle be tomaximize the area for corn?
Quadratic Models Sec 3.4
A farmer has 2000 meters of fencing. He wants to enclose arectangular plot of land to grow corn in.
Inside he also wants to enclose a circular pond with the fence,with the diameter of the pond half the length of the shorter sideof the field.
What should the length and width of the rectangle be tomaximize the area for corn?
Quadratic Models Sec 3.4
A(x)corn ≈ −2x2 + 1000x
-100 100 200 300 400 500 600
-20 000
20 000
40 000
60 000
80 000
100 000
120 000
Quadratic Models Sec 3.4
A window has the shape of a rectangle with an equilateraltriangle on top. If the perimeter of the window is 16 feet, whatdimensions will admit the most light?
Quadratic Models Sec 3.4
A(x) ≈ −x2 + 8x
-10 -5 5 10
5
10
15
Quadratic Models Sec 3.4
Video!
How long do you have until the cow hits you?
Quadratic Models Sec 3.4
Video!
How long do you have until the cow hits you?
Quadratic Models Sec 3.4
Quadratic Models Sec 3.4
Quadratic Models Sec 3.4
Quadratic Models Sec 3.4
Quadratic Models Sec 3.4
Flight of a Baseball
- Effect of the density of the air
On its web page the Colorado Rockies provide the chart shownbelow which shows the effect of altitude on the distance a balltravels.
Distance a batted ball travels (feet) versus altitude above sealevel (feet).
Quadratic Models Sec 3.4
Flight of a Baseball - Effect of the density of the air
On its web page the Colorado Rockies provide the chart shownbelow which shows the effect of altitude on the distance a balltravels.
Distance a batted ball travels (feet) versus altitude above sealevel (feet).
Quadratic Models Sec 3.4
Flight of a Baseball - Effect of the density of the air
On its web page the Colorado Rockies provide the chart shownbelow which shows the effect of altitude on the distance a balltravels.
Distance a batted ball travels (feet) versus altitude above sealevel (feet).
Quadratic Models Sec 3.4
This table summarizes the data given in the graph.
Stadium Altitude (feet) Distance (feet)Yankee Stadium 0 400
Turner Field 1050 408Coors Field 5280 440
Linear model: D(a) = 0.00757267a + 400.02165815
Quadratic model: D(a) = −0.00000001a2 +0.00762979a+400
Quadratic Models Sec 3.4
This table summarizes the data given in the graph.
Stadium Altitude (feet) Distance (feet)Yankee Stadium 0 400
Turner Field 1050 408Coors Field 5280 440
Linear model: D(a) = 0.00757267a + 400.02165815
Quadratic model: D(a) = −0.00000001a2 +0.00762979a+400
Quadratic Models Sec 3.4
Quadratic Models Sec 3.4
Read section 4.1 for Monday.
Quadratic Models Sec 3.4