91Ó°ÊÓ

Solve each equation. $$ 6 x^{2}+72=0 $$

Solve each equation by using the Square Root Property. \(9 x^{2}+30 x+25=11\)

Determine whether each function has a maximum or a minimum value and find the maximum or minimum value. Then state the domain and range of the function. $$ f(x)=2 x+2 x^{2}+5 $$

Solve each equation by using the method of your choice. Find exact solutions. \(21=(x-2)^{2}+5\)

Write each quadratic function in vertex form, if not already in that form. Then identify the vertex, axis of symmetry, and direction of opening. $$ y=4 x^{2}-12 x-11 $$

For Exercises \(43-45,\) use the following information.The girls' softball team is sponsoring a fund-raising trip to see a professional baseball game. They charter a \(60-\) passenger bus for \(\$ 525 .\) In order to make a profit, they will charge \(\$ 15\) per person if all seats on the bus are sold, but for each empty seat, they will increase the price by \(\$ 1.50\) per person. What is the maximum profit the team can make with this fund-raiser, and how many passengers will it take to achieve this maximum?

Determine whether each function has a maximum or a minimum value and find the maximum or minimum value. Then state the domain and range of the function. $$ f(x)=x-2 x^{2}-1 $$

REASONING Examine the graph of \(y=x^{2}-4 x-5\) a. What are the solutions of \(0=x^{2}-4 x-5 ?\) b. What are the solutions of \(x^{2}-4 x-5 \geq 0 ?\) c. What are the solutions of \(x^{2}-4 x-5 \leq 0 ?\)

Find the values of \(m\) and \(n\) that make each equation true. $$ 8+15 i=2 m+3 n i $$

The supporting cables of the Golden Gate Bridge approximate the shape of a parabola. The parabola can be modeled by \(y=0.00012 x^{2}+6,\) where \(x\) represents the distance from the axis of symmetry and \(y\) represents the height of the cables. The related quadratic equation is \(0.00012 x^{2}+6=0\). Calculate the value of the discriminant.