Suppose the graph of revenue as a function of unit price is a parabola that is concave down. What is the significance of the coordinates of the vertex, the x-intercepts, and the y-intercept?
The significance of the coordinates of the vertex, the -intercept and the
-intercept if the graph of revenue as a function of price whose graph of parabola is concave down.
The graph of the revenue as a function of price is a parabola with downward facing.
Consider the Revenue function,
Compare the equation with the standard function and find the value of and .
The values are and .
Here , therefore the parabola will be downward facing and vertex will be the highest point.
Vertex: The formula of p- coordinate or -coordinate of vertex is,
Substitute and in the equation :
This value of gives the highest point on the graph and thus gives the highest value of revenue .
The R- coordinate or -coordinate of vertex is,
Substitute in the function :
Thus -coordinate gives the maximum value of the revenue.
p-intercept or - intercept: To calculate p-intercept of the function, substitute in the equation and solve
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