Yaseen estimates that the monthly demand for her painting kits can be modeled by the function
f(x)=0.02(x-100) ^2, where 0 is less than or equal to x which is less than or equal to 85. The number of kits that Yaseen can supply each month is modeled by the function g(x)=0.01x^2 + 0.5x, where 0 is less than or equal to x which is less than or equal to 100. The value of x represents the quantity of kits and the output of each function is the price.

1) Interpret the domain restrictions on the demand and the supply functions. What do they represent in context of the scenario?

2) Suppose that in her first month Yaseen is able to create 15 kits. How much should she charge
for each of these kits based on her supply function? How much should she charge for each of
these kits based on her demand function? Show your work.

3) In her first month of business, Yaseen sells out of her kits in 3 days. In her second month of
business, she decides to supply 60 kits. How much should she charge for each of these kits based
on her supply function? How much should she charge for each of these kits based on her demand
function? Show your work

4) If Yaseen creates 60 kits in her second month of business and offers them for sale at $66 each,
do you think she will sell all of them? Why or why not

5) What family of functions do f(x) and g(x) belong to? How do you know

6) If you were to graph two quadratic functions on the same xy-plane, how many intersection
points could there be? Use examples to explain your thinking

7) Use algebraic methods to find where Yaseen’s demand and supply functions intersect. What
does this point(s) represent in context of this problem? Show all your work.

8) Confirm your answer from question 7 by using Desmos to create a single graph that shows
both () and () with their domain restrictions. Provide a screenshot of your graph with the
intersection point(s) marked.