Chapter 3, Polynomial and Rational Functions - Section 3.1 - Quadratic Functions and Models - 3.1 Exercises - Page 288: 40

minimum value: $g(7.5)=-5625.$

Let us compare $g(x)=100x^2-1500x$ and $g(x)=ax^2+bx+c$ We can see that $a=100, b=-1500, c=0$. Since $a\gt 0$, the graph opens up. Hence, its vertex is a minimum. The minimum value is at $x=-\frac{b}{2a}=-\frac{-1500}{2\cdot 100}=7.5.$ Hence, the minimum value is $g(7.5)=100(7.5)^2-1500(7.5)=-5625.$