Chapter 9.4, Problem 1MP

(a)

To determine

To write the function for the area of rectangular sign in factored form.

Answer to Problem 1MP

  $A(x)=2x\left(-\frac{x}{3}+6\right)$

Explanation of Solution

Given:

The following equation shows the function $A\left(x\right)$ that represents the area of rectangular sign

  $-\frac{2x^2}{3}+12x$

Calculation:

The factored form of the function will be-

  $A(x)=2x\left(-\frac{x}{3}+6\right)$

(b)

To determine

To find the zeroes of the function.

Answer to Problem 1MP

  $x=0,x=18$

Explanation of Solution

The zeroes of the function can be found as follows-

  $\begin{array}{l}A(x)=2x\left(-\frac{x}{3}+6\right)\\ 2x=0,\frac{-x}{3}=-6\\ x=0,x=18\end{array}$

(c)

To determine

To find out the maximum area of the rectangular sign with the help of zeroes.

Answer to Problem 1MP

  $54$ Square unit.

Explanation of Solution

The following is the graph of the function area-

Here, the maximum area is $54$ square unit.