91Ó°ÊÓ

Write each function in standard form. $$ y=2 x(x+7)+8 x $$

A rock club's profit from booking local bands depends on the ticket price. Using past recipts the owners find that the profit \(p\) can be modeled by the function \(p=-15 t^{2}+600 t+50,\) where trepresents the ticket price in dollars. a. What price yields the maximum profit? b. What is the maximum profit? c. Open-Ended What price would you pay to see your favorite local band? How much profit would the club owner make using that ticket price?

Factor each expression completely. $$ 64 t^{2}-16 $$

Critical Thinking The graphs of each pair of functions intersect. Find their points of intersection without using a calculator. Hint: Solve as a system using substitution. $$ \begin{array}{l}{y=x^{2}} \\ {y=-\frac{1}{2} x^{2}+\frac{3}{2} x+3}\end{array} $$

Solve each quadratic equation by completing the square. $$ 3 x^{2}+x=\frac{2}{3} $$

Solve each system by elimination. $$ \left\\{\begin{array}{l}{2 x-3 y=-14} \\ {3 x-y=7}\end{array}\right. $$

Write each function in standard form. $$ y=\frac{1}{2}(x-5)^{2}+5 $$

Solve each system by elimination. $$ \left\\{\begin{array}{l}{x-3 y=2} \\ {x-2 y=1}\end{array}\right. $$

Write each function in standard form. $$ y=-0.1(10 x+20)^{2} $$

Multiple Choice In a complex number plane, what geometric figure describes the complex numbers with absolute value 10\(?\) $$ \begin{array}{ll}{\text { A square }} & {\text { B circle }} \\ {\text { C line }} & {\text { D two points }}\end{array} $$