Question

The demand function for a product is quadratic. Three points which lies on the function are (10, 1800), (20, 1200), and (30, 500). Determine the equation for the demand function. What quantity will be demanded at a price $20?

Answer 1

I'm not 100% sure on this one, but I'll give it my best try

recall that a quadratic equation takes the form
y = ax^2 + bx + c

for each point, plug in the x and y values
ex: (10, 1800) becomes 1800 = a(10^2) + b(10) + c
and repeat this logic for the rest of the points

once you have three equations, with three unknowns, you can set up a system of equations, and solve through elimination/substitution/matrix equations, etc.

now, the second part of the question I'm not entirely sure about - judging by the numbers, I'm not entirely sure which axis is supposed to represent demand and which one is price - my first thought was the x-axis representing price, but the second part of the question is asking for demand at $20 which would already be given if we define demand as x

Answer 2

@semidefinite would you mind checking my work, especially the 2nd part of this question? sorry if this is a trivial question, but I don't have much econ background