EC4004 Quadratic Equations Assignment

1. For each of the following find:
   1. The y-intercept
   2. The roots (if any) of the equation.
   3. Sketch the curve

      (a) y = x²

      (b) y = x² + 4

      (c) y = 3x² - 6x - 4

      (d) y = -2x² - 8x + 24

      (e) y = x² + 6x + 9

2. A firm’s total Revenue (TR) depends on its level of output (Q). Hence TR = f(Q). If the price of the output is denoted P, then the TR is always P x Q.
   • You should be able to recognize that this is a linear function with an intercept of 50 and a slope of –2.
   • The TR = P x Q = (50 – 2Q).Q. Hence, 2 + 50. Sketch the graph of this TR line and find the roots. Hint: put TR on the vertical axis and Q on the horizontal.
3. Sketch the graph of a total cost (TC) function: 2 + 10
4. Demand and supply curves are not usually linear (although they are often drawn that way). Sketch the following demand and supply curves on a single graph:

   Demand: P_D = -Q² + 4

   Supply: Ps = Q² -0.5

Note: you only need the positive part of the graph for this sketch. Try and work out the point at which the graphs intersect (equilibrium price and quantity).