91Ó°ÊÓ

An athlete whose event is the shot put releases the shot wilh the same initial velocity but at different angles. The figure shows the parabolic paths for shots released at angles of \(35^{\circ}\) and \(65^{\circ} .\) Exercises \(57-58\) are based on the functions that model the parabolic paths. (table cannot copy) You have 80 yards of fencing to enclose a rectangular region. Find the dimensions of the rectangle that maximize the enclosed area. What is the maximum area?

A stand-up comedian uses algebra in some jokes, including one about a telephone recording that announces "You have just reached an imaginary number. Please multiply by \(i\) and dial again." Explain the joke.

Explain why the equation \(x^{4}+6 x^{2}+2=0\) has no rational roots.

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. Synthetic division can be used to find the quotient of \(10 x^{3}-6 x^{2}+4 x-1\) and \(x-\frac{1}{2}.\)

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. Any problem that can be done by synthetic division can also be done by the method for long division of polynomials.

Find \(k\) so that \(4 x+3\) is a factor of $$20 x^{3}+23 x^{2}-10 x+k$$

Write equations for several polynomial functions of odd degree and graph each function. Is it possible for the graph to have no real zeros? Explain. Try doing the same thing for polynomial functions of even degree. Now is it possible to have no real zeros?

Use synthetic division to show that 5 is a solution of $$x^{4}-4 x^{3}-9 x^{2}+16 x+20=0$$ Then solve the polynomial equation.

What do we mean when we describe the graph of a polynomial function as smooth and continuous?

Explain how to decide whether a parabola opens upward or downward.