<PRE><B>Question 1163385</B>
&lt;br&gt;
The function is quadratic:&lt;br&gt;
{{{q(p) = ap^2+bp+c}}}&lt;br&gt;
Use the three given points to form three equations in the unknowns a, b, and c.&lt;br&gt;
{{{3600a+60b+c = 2750}}}
{{{4900a+70b+c = 6000}}}
{{{6400a+80b+c = 9750}}}&lt;br&gt;
Eliminate c between the first and second equations, and between the second and third:&lt;br&gt;
{{{1300a+10b = 3250}}}
{{{1500a+10b = 3750}}}&lt;br&gt;
Eliminate b between those two equations:&lt;br&gt;
{{{200a = 500}}}
{{{a = 2.5}}}&lt;br&gt;
Plug a=2.5 in either of the previous two equations to find b=0.&lt;br&gt;
Plug a=2.5 and b=0 in any of the original equations to find a=-6250.&lt;br&gt;
a) ANSWER: The supply function is f(p) = 2.5p^2-6250&lt;br&gt;
b) Mathematically, a negative price doesn&#39;t make sense -- so the restriction on the domain is p greater than or equal to 0.&lt;br&gt;
But realistically a negative quantity supplied doesn&#39;t make sense either.  f(50)=0, so realistically the restriction on the domain is p greater than or equal to 50.&lt;br&gt;
c) The p-intercept is when q=0, which is (50,0).  That means no products will be supplied when the price is $50.&lt;br&gt;
d) q(75) = 7812.5.  I&#39;m not sure whether in the real world you would mean the quantity supplied at a price of $75 is 7812 or 7813....&lt;br&gt;
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