Answer:
[tex]A.\ \ r(d)=-100(d-25)^2+122,500[/tex]
Step-by-step explanation:
Here r(d) represents the monthly revenue, in dollars, from selling skateboards when the price of a skateboard has been decreased by a specific amount d times.
As r(d) is a quadratic function, it represents a parabola. When the parabola opens downwards, at the vertex the value of the function is the maximum value of the function.
The vertex form of parabola with vertex at [tex](h, k)[/tex] is,
[tex]y=a(x-h)^2+k[/tex]
The standard form of parabola is,
[tex]y=ax^2+bx+c[/tex]
where vertex is [tex]\left(-\dfrac{b}{2a},y\left(-\dfrac{b}{2a}\right)\right)[/tex]
In equation 1, the leading coefficient or the coefficient of maximum power i.e d² will be negative, so it opens downward and focus is at [tex](25, 122,500)[/tex] Hence, the maximum revenue earned will be $122,500.
But all the remaining cases you have to take them to standard form then only applying formula you can get the coordinates of vertex.
Therefore, equation A representation of the revenue function would be most helpful.
