A parabola is symmetric about its axis of symmetry
Two important questions:
For which values of \(x\) does \(ax^2+bx+c=0\)?
What are the coordinates of the minimum (maximum) of the parabola (its vertex)?
Examples
\(f\left(x\right)=x^2-4x+3\)
Answer question 1
Take the following example. An industry is characterized by an industry-demand function \(D:\ P=102-2Q\). The cost curve of a firm within this industry is given by \(C:\ C=2q+.5q^2\). Find the profits of this firm.
The monopolist's profit function is given by: \(\Pi=102Q-2Q^2-2Q-.5Q^2=100Q-2.5Q^2\). \(\Pi=0\) if \(Q=0,\ 40\). Thus, \(\Pi\) is maximized at \(Q=20\).