We are given that the function of demand is given as:
[tex]x=-8p+400[/tex]
Where:
[tex]\begin{gathered} x=\text{ quantity demanded} \\ p=\text{ price} \end{gathered}[/tex]
The function of revenue is given by:
[tex]R=px=p\left(-8p+400\right)[/tex]
Applying the distributive law we get:
[tex]R=-8p^2+400p[/tex]
We get an equation of the form:
[tex]R=ap^2+bp+c[/tex]
This is a quadratic equation and its graph is a parabola.
If the value of "a" is negative this means that the parabola opens downwards, therefore, the possible answers are A or D.
We notice that A is the graph of p vs R. Since our equation is a function of "p" we need R vs P, therefore, the right answer must be D.
