Chapter 4 - Section 4.3 - Quadratic Functions and Their Properties - 4.3 Assess Your Understanding - Page 301: 88

a) $20000$ b)$2000$

Let's compare $f(x)=5x^2-200x+4000$ to $f(x)=ax^2+bx+c$. We can see that a=5, b=-200, c=4000. a>0, hence the graph opens up, hence its vertex is a minimum. The minimum value is at $x=-\frac{b}{2a}=-\frac{-200}{2\cdot 5}=20.$ Hence the minimum value is $f(20)=5(20)^2-200(20)+4000=2000.$ Thus: a) $20000$ b)$2000$