# exponential form, polynomial, asymptote

(a) = _______ (fill in the blank)

(b) Let . Write the exponential form of the equation and solve the equation for x.

A farmer has 60 feet of fencing with which to enclose a rectangular pen adjacent to a long existing wall. He will use the wall for one side and the available fencing for the remaining three sides.

If the sides perpendicular to the wall have length x feet, the area A of the enclosure is given by
A(x) = -2x2 + 60x.

This area function is a quadratic function and so its graph is a parabola.

(a) Does the parabola open up or down? __________

(b) Find the vertex of the quadratic function A(x). Show work.

(c) Use the work in the previous parts to help determine the dimensions of the enclosure which yield the maximum area, and state the maximum area. (Fill in the blanks below. Include the units of measurement.)

The maximum area is ______________,

when the sides perpendicular to the wall have length x = ___________

and the side parallel to the wall has length ___________ .

Consider the polynomial f(x) = 3x3 + 13x2 - 11x - 5.

Find all of the zeros of the given polynomial. Be sure to show work, explaining how you have found the zeros.

Lee is a salesperson who must decide between two monthly income options:
Option A: Salary of \$1680 per month, plus 8% of monthly sales
or Option B: Salary of \$2000 per month, plus 6% of monthly sales

For what amount of monthly sales is Option A the better choice for Lee than Option B?
Show work. Write an appropriate inequality and solve it. Write a sentence to answer the question.

Let .

(a) State the vertical asymptote(s).

(b) State the horizontal asymptote.

(c) Find the inverse function of f. Show work.

Solve and check all proposed solutions. .
Show work for solving and for checking.

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#### Solution Preview

...e parabola opens up (it has a minima).
In our case
We shall rewrite the function in its canonical form:

It is obvious that the function will attain a maxima when the quadratic term is zero, or , and the maximal value of the function at that point is
In our case we get:

So the maximum occurs when
The value of the function at that point is
Thus the vertex is
The maximum area is 450
The sides perpendicular to the wall has the length:
The side parallel to the wall has the length
The dimensions of the fence are length of 30m and width of 15m.

(4)
We factor the polynomial. From examining the coefficients,we see that is a solution for the equation:

So we ...