This is known as the absolute maximum. The highest point, aka the vertex, represents the largest profit possible. Profit functions are often parabolas that open downwards, though other types of profit functions may be possible.
The initial profit is when x = 0, which is the y intercept (where the graph crosses the y axis). The x intercepts are when the profit is y = 0 (where the graph crosses the x axis). Whenever the profit is 0, this is considered a break-even point.
Each and every aspect of the graph of a profit function was discussed thoroughly.
We know the graph of the profit function is parabolic in nature.
A parabola is a U-shaped curve derived from a cone when we cut a cone by a plane that is at the same slant as the side of the cone.
A) The lowest point of an upward parabola(a>0) [tex]y=ax^{2} +bx+c[/tex] is [tex](\frac{-b}{2a} ,\frac{4ac-b^{2} }{4a})[/tex].
B) The point where the graph crosses the x-axis is called the roots or zeros of a quadratic equation, also called the break-even point.
C)The point where the graph crosses the y-axis is called the constant term i.e. [tex]c[/tex] of a quadratic equation [tex]ax^{2} +bx+c=0[/tex].
D)The highest point of the graph of the parabola [tex]ax^{2} +bx+c=0[/tex] (if a>0)does not exist, however, if it is a downward parabola (a<0), the highest point is[tex](\frac{-b}{2a} ,\frac{4ac-b^{2} }{4a})[/tex].
Thus, each and every aspect of the graph of a profit function was discussed thoroughly.
To get more about a parabola visit:
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