Quadratic Functions and Models

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February 10th 2009, 05:50 AM
jnm07

Quadratic Functions and Models

I think i messed up somewhere in this problem, or I'm doing it wrong. Can some please help me figure it out, get me back on track or explain what I did wrong...

The average weight of a sedan could be approximated by
W= 6(t^2) - 240t +4800 (5< t <27)

where t is its year of manufacture (t= 0 represents 1970) and W is the average weight of a sedan in pounds. Sketch the graph of W as a function of t. According to the model, in what year were sedans the lightest? What was their average weight in that year?

I have:
W= 6(t^2) - 240t +4800

vertex: (20, 2400)
-b/2a = 240/12 = 20

6(20^2) - 240(20) +4800
= 2400

Then I tried plugging into the quadratic equation to find the x intercepts or roots and I got 54.6 and -14.6
February 10th 2009, 08:56 AM
Tarzan

Quote:

Originally Posted by jnm07

I think i messed up somewhere in this problem, or I'm doing it wrong. Can some please help me figure it out, get me back on track or explain what I did wrong...

The average weight of a sedan could be approximated by
W= 6(t^2) - 240t +4800 (5< t <27)

where t is its year of manufacture (t= 0 represents 1970) and W is the average weight of a sedan in pounds. Sketch the graph of W as a function of t. According to the model, in what year were sedans the lightest? What was their average weight in that year?

I have:
W= 6(t^2) - 240t +4800

vertex: (20, 2400)
-b/2a = 240/12 = 20

6(20^2) - 240(20) +4800
= 2400

Then I tried plugging into the quadratic equation to find the x intercepts or roots and I got 54.6 and -14.6

You got the vertex right but the graph never crosses the x axis, (the car is never going to weigh 0lb) the vertex is a minima. It's an approximate x^2 graph crosses the y axis when t=0 - find W

How did you find those points you gave? - if you used the quadratic formula remember you can't have the square root of a negative number.
February 10th 2009, 08:59 AM
mollymcf2009

Quote:

Originally Posted by jnm07

I think i messed up somewhere in this problem, or I'm doing it wrong. Can some please help me figure it out, get me back on track or explain what I did wrong...

The average weight of a sedan could be approximated by
W= 6(t^2) - 240t +4800 (5< t <27)

where t is its year of manufacture (t= 0 represents 1970) and W is the average weight of a sedan in pounds. Sketch the graph of W as a function of t. According to the model, in what year were sedans the lightest? What was their average weight in that year?

I have:
W= 6(t^2) - 240t +4800

vertex: (20, 2400)
-b/2a = 240/12 = 20

6(20^2) - 240(20) +4800
= 2400

Then I tried plugging into the quadratic equation to find the x intercepts or roots and I got 54.6 and -14.6

2400 is correct. This function does not have any x intercepts, it is a parabola and the vertex of the parabola (when cars weighed the least) is at y = 2400, this is your average weight for the year.

$2400 = 6t^2 - 240t + 4800$

$0 = 6t^2 -240t + 2400$

Then do your quadratic. This will give you the year.