SOLUTION: Write an equation to represent the data shown in the table below. x | y -2 , 152 -1 , 76 0 , 38

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Question 1131533: Write an equation to represent the data shown in the table below.
x | y
-2 , 152
-1 , 76
0 , 38
Found 3 solutions by MathLover1, Alan3354, greenestamps:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
Write an equation to represent the data shown in the table below.
x | y
-2 | 152
-1 |76
0 | 38

y=ax%5E2-bx%2Bc
since given (0 , 38)=>c=38
y=ax%5E2-bx%2B38..........use point -1 , 76
76=a%28-1%29%5E2-b%28-1%29%2B38
76-38=a%2Bb
a%2Bb=38
b=38-a........(1)

y=ax%5E2-bx%2B38..........use -2 , 152
152=a%28-2%29%5E2-b%28-2%29%2B38
152-38=4a%2B2b
114=4a%2B2b
57=2a%2Bb
b=57-2a.......(2)

from (1) and (2) we have

38-a=57-2a
2a-a=57-38
a=19
then
b=38-19........(1)
b=19


and your equation is:
y=19x%5E2-19x%2B38




Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Write an equation to represent the data shown in the table below.
x | y
-2 , 152
-1 , 76
0 , 38
===========
There are an infinite # of them.
The other tutor showed a parabola.
A circle can be found, and an infinite # of ellipses.

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


Continuing the response from tutor @alan3354, there are also an infinite number of polynomial equations that are satisfied by the three given data points.

However, since the value is cut in half for each increase of 1 in the x value, an exponential function would seem the most appropriate: y+=+ab%5Ex.

The constant factor in the given sequence is 1/2 or 0.5: y+=+a%28.5%29%5Ex

When x is 0, y is 38:
38+=+a%28.5%29%5E0+=+a

So the exponential function for the given points is

y+=+38%28.5%29%5Ex