Chapter 3 - Section 3.1 - Quadratic Functions and Models - 3.1 Exercises - Page 253: 63

$(a)$ $A(x)=-x^2+1200x$ $(b)$ $600ft$ by $600ft$

$(a)$ Area of a rectangle is $width \times length$, that is : $A(x)=x(1200-x)=-x^2+1200x$ $A(x)=-x^2+1200x$ $(b)$ To calculate the maximum value of the area, we can use the following formula $x=-\frac{b}{2a}$ We have : $a=-1$ $b=1200$ $x=-\frac{1200}{-2}=600$ We have dimensions $600ft$ by $600ft$