Question 1042307
it took some doing, but i think i found the answer.
the answer is y = .0005 * x^2 + 50,000


the graph of that equation looks like this:


<img src = "http://theo.x10hosting.com/2016/073102.jpg" alt="$$$" </>


the procedure is as follows:


the general form of a quadratic equation is:


y = ax^2 + bx + c


when y = 100,000 and x = 10,000, and c = 50,000, the equation becomes:


100,000 = 10,000^2 * a + 10,000 * b + 50,000


when y = 250,000 and x = 20,000, and c = 50,000, the equation becomes:


250,000 = 20,000^2 * a + 20,000 * b + 50,000


subtract 50,000 from both sides of each equation and you get:


50,000 = 10,000^2 * a + 10,000 * b
200,000 = 20,000^2 * a + 20,000 * b


multiply both sides of the first equation by 2 and you get:


100,000 = 2 * 10,000^2 * a + 2 * 10,000 * b
200,000 = 20,000^2 + a + 20,000 * b


simplify the first equation and leave the second equation as is to get:


100,000 = 2 * 10,000^2 * a + 20,000 * b
200,000 = 20,000^2 * a + 20,000 * b


subtract the first equation from the second equation to get:


100,000 = 20,000^2 * a - 2 * 10,000^2 * a


simplify to get:


100,000 = 200,000,000 * a


divide both sides of the equation by 200,000,000 to get:


100,000 / 200,000,000 = a


solve for a to get:


a = .0005


go back to the first original equation of 50,000 = 10,000^2 * a + 10,000 * b and replace a with .0005 and solve for b to get b = 0.


you have a = .0005 and b = 0 and c = 50,000


the general equation of y = ax^2 + bx + c becomes:


y = .0005x^2 + 0x + 50,000 which becomes:


y = .0005x^2 + 50,000