91Ó°ÊÓ

Maximum Revenue The total revenue \(R\) earned per day (in dollars) from a pet-sitting service is given by \(R(p)=-12 p^{2}+150 p,\) where \(p\) is the price charged per pet (in dollars). (a) Find the revenues when the prices per pet are \(\$ 4\) \(\$ 6,\) and \(\$ 8 .\) (b) Find the unit price that will yield a maximum revenue. What is the maximum revenue? Explain your results.

Complex Solutions of a Quadratic Equation. Use the Quadratic Formula to solve the quadratic equation $$4.5 x^{2}-3 x+12=0$$

Simplify the rational expression by using long division or synthetic division. \(\frac{x^{4}+6 x^{3}+11 x^{2}+6 x}{x^{2}+3 x+2}\)

Find the value of \(k\) such that \(x-4\) is a factor of \(x^{3}-k x^{2}+2 k x-8.\)

Error Analysis Describe the error. $$\sqrt{-6} \sqrt{-6}=\sqrt{(-6)(-6)}=\sqrt{36=6}$$

Modeling Polynomials Sketch the graph of a polynomial function that is of fourth degree, has a zero of multiplicity \(2,\) and has a negative leading coefficient. Sketch the graph of another polynomial function with the same characteristics except that the leading coefficient is positive.

Modeling Polynomials Sketch the graph of a polynomial function that is of fifth degree, has a zero of multiplicity \(2,\) and has a negative leading coefficient. Sketch the graph of another polynomial function with the same characteristics except that the leading coefficient is positive.