SOLUTION: Let x be the numbet of years since 1980 and y be the life expectancy for a person born between ( 1980 + x ) and ( 1980 + x + 5 ). Find the quadratic equation whose graph passess th

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Let x be the numbet of years since 1980 and y be the life expectancy for a person born between ( 1980 + x ) and ( 1980 + x + 5 ). Find the quadratic equation whose graph passess th      Log On


   



Question 1163445: Let x be the numbet of years since 1980 and y be the life expectancy for a person born between ( 1980 + x ) and ( 1980 + x + 5 ). Find the quadratic equation whose graph passess through the points ( 0, 78,2) , ( 5, 79) and ( 10, 79.2 )
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52784) About Me  (Show Source):
You can put this solution on YOUR website!
.

This object in parentheses (0,78,2) is not a point in a plane.


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To solve the problem successfully,  first,  you  (the visitor)  should write the problem correctly.

The second is to  FORGET  about this wording definition of the function in the first part of the problem,
and concentrate your attention on parabola only.


The first part of the problem's description is a typical  "noise",  whose destination is to distract
the reader attention and to confuse him.

Do not be amazing :  some problems are specially constructed in this way,  so you should be ready to it
and should be aware about it.

The rest is just a technique.


/\/\/\/\/\/

The lesson to learn from the solution is  THIS :

            In such problems,  it is vitally important to separate parts of the description
            that are a  "noise",  and forget about them.



Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Let x be the numbet of years since 1980 and y be the life expectancy for a person born between ( 1980 + x ) and ( 1980 + x + 5 ). Find the quadratic equation whose graph passess through the points cross%28%22%28+0%2C+78%2C2%29%22%29 (0,78.2), ( 5, 79) and ( 10, 79.2 )

The general quadratic function is

y+=+ax%5E2%2Bbx%2Bc

Use the three given data points in that equation to form three equations in the coefficients a, b, and c.

a%280%5E2%29%2Bb%280%29%2Bc+=+78.2
(1) c+=+78.2

a%285%5E2%29%2Bb%285%29%2Bc+=+79
(2) 25a%2B5b%2Bc+=+79

a%2810%5E2%29%2Bb%2810%29%2Bc+=+79.2
(3) 100a%2B10b%2Bc+=+79.2

Substitute (1) into (2) and (3) to get two equations in a and b.

(4) 25a%2B5b+=+0.8
(5) 100a%2B10b+=+1

Subtract (4) from (5).

{6) 75a%2B5b+=+0.2

Subtract (4) from (6).

50a+=+-0.6

(7) a+=+-0.012+=+-3%2F250

Substitute in (4) to find b.

25%28-3%2F250%29%2B5b+=+0.8
-3%2F10+%2B+5b+=+8%2F10
5b+=+11%2F10
b+=+11%2F50

ANSWER: The quadratic equation is

y+=+%28-3%2F250%29x%5E2%2B%2811%2F50%29x%2B78.2