91Ó°ÊÓ

The phrase "y varies directly with \(x\) " is written \(y=k x,\) where \(k\) is called the ____ of variation.

Discuss/Explain each of the following: (a) irreducible quadratic factors, (b) factors that are complex conjugates, (c) zeroes of multiplicity \(m\), and (d) upper bounds on the zeroes of a polynomial.

Wages earned varies directly with the number of hours worked. Last week I worked 37.5 hr and my gross pay was 344.25 dollars. Write the variation equation and determine how much I will gross this week if I work 35 hr. What does the value of \(k\) represent in this case?

State the end behavior and \(y\) -intercept of the functions given. Do not graph. $$g(x)=x^{4}-4 x^{3}-2 x^{2}+16 x-12$$

Find a polynomial \(P(x)\) having real coefficients, with the degree and zeroes indicated. Assume the lead coefficient is 1. Recall \((a+b i)(a-b i)=a^{2}+b^{2}\). degree \(3, x=3, x=2 i\)

Solve each quadratic inequality by locating the \(x\) -intercept(s) (if they exist), and noting the end behavior of the graph. Begin by writing the inequality in function form as needed. $$h(x)=-x^{2}+14 x-49 ; h(x)<0$$

Solve each quadratic inequality by locating the \(x\) -intercept(s) (if they exist), and noting the end behavior of the graph. Begin by writing the inequality in function form as needed. $$-x^{2}>2$$

Solve each quadratic inequality by locating the \(x\) -intercept(s) (if they exist), and noting the end behavior of the graph. Begin by writing the inequality in function form as needed. $$-x^{2}+3 x<3$$

Maximum profit: An automobile manufacturer can produce up to 300 cars per day. The profit made from the sale of these vehicles can be modeled by the function \(P(x)=-10 x^{2}+3500 x-66,000\) where \(P(x)\) is the profit in dollars and \(x\) is the number of automobiles made and sold. Based on this model: a. Find the \(y\) -intercept and explain what it means in this context. b. Find the \(x\) -intercepts and explain what they mean in this context. c. How many cars should be made and sold to maximize profit? d. What is the maximum profit?

Use the remainder theorem to evaluate \(P(x)\) as given. \(P(x)=-2 x^{3}+9 x^{2}-11\) a. \(P(-2)\) b. \(P(-1)\)