Question 80009
<pre><font face = "lucida console" size = 4><b>
Can you please help me write a quadratic function 
with this set of data? 
(0,254)(4,234)(8,235)(12,239)(16,255) 

f(0) = 254
f(4) = 234
f(8) = 235
f(12) = 239

There is a terribly long formula for finding the 
quadratic regression formula.  When you plug 
into it you get:

y = f(x) = 75/224x² - 1451/280x + 1769/7 

Are you allowed to use a TI-83 or TI-84?  If so, then

press STAT then ENTER, 
enter the five x values under L1 and the five values for f(x) in L2.

press STAT then the right arrow then 5, then ENTER

You see:

y = ax²+bx+c
a=.3348214286
b=-5.182142857
c = 252.7142657
R²=.9564574654

Since R² is near 1, the fit is good.

plug those values into 

y = ax²+bx+c

y = f(x) = .3348214286x² - 5.182142857x + 252.7142857

Here's the graph of that, the o's are your 5 points above:

{{{drawing(500,300, -1.6,17.6,230.43,258.57,
  graph(500,300, -1.6,17.6,230.43,258.57,(75/224)x^2-(1451/280)x+1769/7 ),
           locate(0,254,o),
           locate(4,235,o),
           locate(8,235,o),
           locate(12,240,o),
           locate(16,257,o) 

) }}}

{{{graph(500,10, -1.6,17.6,-100,1)}}}

Edwin</pre>