Chapter 8

Find the maximum or minimum value of \(y\) for each function. $$y=33-x^{2}$$

Solve each inequality. State the solution set using interval notation when possible. \(x^{2}>0\)

Find the maximum or minimum value of \(y\) for each function. $$y=-3 x^{2}+14$$

Solve each inequality. State the solution set using interval notation when possible. \(x^{2} \geq 0\)

Find the maximum or minimum value of \(y\) for each function. $$y=6+5 x^{2}$$

Solve each inequality. State the solution set using interval notation when possible. \(x^{2}+4 \geq 0\)

Find the maximum or minimum value of \(y\) for each function. $$y=x^{2}+2 x+3$$

Find all real solutions to each equation. $$x^{-2}+x^{-1}-6=0$$

Solve each inequality. State the solution set using interval notation when possible. \(x^{2}+1 \leq 0\)

Find the maximum or minimum value of \(y\) for each function. $$y=x^{2}-2 x+5$$

Find all real solutions to each equation. $$x^{-2}-2 x^{-1}=8$$

Solve each inequality. State the solution set using interval notation when possible. \(\frac{1}{x}<0\)

Find the maximum or minimum value of \(y\) for each function. $$y=-2 x^{2}-4 x$$

Find all real solutions to each equation. $$x^{1 / 6}-x^{1 / 3}+2=0$$

Solve each inequality. State the solution set using interval notation when possible. \(\frac{1}{x^{2}}=0\)

Find the maximum or minimum value of \(y\) for each function. $$y=-3 x^{2}+24 x$$

Find all real solutions to each equation. $$x^{2 / 3}-x^{1 / 3}-20=0$$

Solve each inequality. State the solution set using interval notation when possible. \(x^{2} \leq 9\)

Solve each problem. If a baseball is projected upward from ground level with an initial velocity of 64 feet per second, then its height is a function of time, given by \(s(t)=-16 t^{2}+64 t .\) Graph this function for \(0 \leq t \leq 4\). What is the maximum height reached by the ball?

Solve each equation by an appropriate method. $$\sqrt{2 x+1}=x-1$$

Find all real solutions to each equation. $$\left(\frac{1}{y-1}\right)^{2}+\left(\frac{1}{y-1}\right)=6$$

Solve each inequality. State the solution set using interval notation when possible. \(x^{2} \geq 36\)

Solve each problem. If a soccer ball is kicked straight up with an initial velocity of 32 feet per second, then its height above the earth is a function of time given by \(s(t)=-16 t^{2}+32 t .\) Graph this function for \(0 \leq t \leq 2\). What is the maximum height reached by this ball?

Solve each equation by an appropriate method. $$\sqrt{2 x-4}=x-14$$

Find all real solutions to each equation. $$\left(\frac{1}{w+1}\right)^{2}-2\left(\frac{1}{w+1}\right)-24=0$$

Solve each inequality. State the solution set using interval notation when possible. \(16-x^{2}>0\)

Solve each problem. Minimum cost. It costs Acme Manufacturing \(C\) dollars per hour to operate its golf ball division. An analyst has determined that \(C\) is related to the number of golf balls produced per hour, \(x,\) by the equation \(C=0.009 x^{2}-\) \(1.8 x+100 .\) What number of balls per hour should Acme produce to minimize the cost per hour of manufacturing these golf balls?

Solve each equation by an appropriate method. $$w=\frac{\sqrt{w+1}}{2}$$

Find all real solutions to each equation. $$2 x^{2}-3-6 \sqrt{2 x^{2}-3}+8=0$$

Solve each inequality. State the solution set using interval notation when possible. \(9-x^{2}<0\)

Solve each problem. A chain store manager has been told by the main office that daily profit, \(P\), is related to the number of clerks working that day, \(x,\) according to the equation \(P=-25 x^{2}+300 x .\) What number of clerks will maximize the profit, and what is the maximum possible profit?

Solve each equation by an appropriate method. $$y-1=\frac{\sqrt{y+1}}{2}$$

Find all real solutions to each equation. $$x^{2}+x+\sqrt{x^{2}+x}-2=0$$

Solve each inequality. State the solution set using interval notation when possible. \(x^{2}-4 x \geq 0\)

Solve each problem. Maximum area. Jason plans to fence a rectangular area with 100 meters of fencing. He has written the formula \(A=w(50-w)\) to express the area in terms of the width \(w\). What is the maximum possible area that he can enclose with his fencing?

Solve each equation by an appropriate method. $$\frac{t}{t-2}=\frac{2 t-3}{t}$$

Find all real solutions to each equation. $$x^{-2}-2 x^{-1}-1=0$$

Solve each inequality. State the solution set using interval notation when possible. \(4 x^{2}-9>0\)

Solve each problem. A company uses the function \(C(x)=\) \(0.02 x^{2}-3.4 x+150\) to model the unit cost in dollars for producing \(x\) stabilizer bars. For what number of bars is the unit cost at its minimum? What is the unit cost at that level of production?

Solve each equation by an appropriate method. $$\frac{z}{z+3}=\frac{3 z}{5 z-1}$$

Find all real solutions to each equation. $$x^{-2}-6 x^{-1}+6=0$$

Use the quadratic formula and a calculator to solve each equation. Round answers to three decimal places and check your answers. $$x^{2}+3.2 x-5.7=0$$

Solve each inequality. State the solution set using interval notation when possible. \(3\left(2 w^{2}-5\right)

Solve each problem. The amount of nitrogen dioxide \(A\) in parts per million (ppm) that was present in the air in the city of Homer on a certain day in June is modeled by the function$$A(t)=-2 t^{2}+32 t+12$$where \(t\) is the number of hours after 6: 00 A.M. Use this function to find the time at which the nitrogen dioxide level was at its maximum.

Solve each equation by an appropriate method. $$\frac{2}{x^{2}}+\frac{4}{x}+1=0$$

Find all real and imaginary solutions to each equation. $$w^{2}+4=0$$

Use the quadratic formula and a calculator to solve each equation. Round answers to three decimal places and check your answers. $$x^{2}+7.15 x+3.24=0$$

Solve each inequality. State the solution set using interval notation when possible. \(6\left(y^{2}-2\right)+y<0\)

Solve each equation by an appropriate method. $$\frac{1}{x^{2}}+\frac{3}{x}+1=0$$

Find all real and imaginary solutions to each equation. $$w^{2}+9=0$$