Chapter 9

Using the fact that \(x^{1 / 2}=\sqrt{x}\), rewrite in simplest radical form. $$x^{1 / 2} \cdot 4 \sqrt{2}$$

SKETCHING GRAPHS Sketch the graph of the function. Label the vertex. $$ y=-\frac{1}{2} x^{2}-4 x+6 $$

Solve the equation or write no solution. Write the solutions as integers if possible. Otherwise write them as radical expressions. $$5 x^{2}+5=20$$

Solve the quadratic equation by finding square roots or by using the quadratic formula. Explain why you chose the method. $$x^{2}-625=0$$

The solution of a quadratic equation can be found by graphing each side separately and locating the points of intersection. You may wish to consult page 532 for help in approximating solutions. $$ -4.87 x^{2}+1.44 x=5.22 x^{2}+6 x $$

Use the quadratic formula to solve the equation. $$2 x^{2}-2 x-12=0$$

Using the fact that \(x^{1 / 2}=\sqrt{x}\), rewrite in simplest radical form. $$18^{1 / 2} x \cdot 9 x^{1 / 2} x$$

SKETCHING GRAPHS Sketch the graph of the function. Label the vertex. $$ y=-\frac{1}{4} x^{2}-x-1 $$

Solve the quadratic equation by finding square roots or by using the quadratic formula. Explain why you chose the method. $$4 y^{2}-49=0$$

Solve the system of linear equations if possible. Does the system have exactly one solution, no solution, or infinitely many solutions? $$ \begin{aligned}&-2 x+8 y=11\\\&x+6 y=2\end{aligned} $$

Use a table of values to graph the equation. $$y=-x+5$$

Use the quadratic formula to solve the equation. $$-\frac{2}{3} x^{2}-3 x+1=0$$

In Exercises 65 and 66 use the following information. A bottlenose dolphin jumps out of the water. The path the dolphin travels can be modeled by \(h=-0.2 d^{2}+2 d,\) where \(h\) represents the height of the dolphin and \(d\) represents horizontal distance. What is the maximum height the dolphin reaches?

Solve the equation or write no solution. Write the solutions as integers if possible. Otherwise write them as radical expressions. $$x^{2}+4.0=0$$

Solve the quadratic equation by finding square roots or by using the quadratic formula. Explain why you chose the method. $$-2 x^{2}+6 x+1=0$$

Solve the system of linear equations if possible. Does the system have exactly one solution, no solution, or infinitely many solutions? $$ \begin{aligned}&4 x+5 y=37\\\&-5 x+3 y=0\end{aligned} $$

Use a table of values to graph the equation. $$y=x-7$$

Use the quadratic formula to solve the equation. $$-7 x^{2}-2.5 x+3=0$$

Solve the equation or write no solution. Write the solutions as integers if possible. Otherwise write them as radical expressions. $$6 x^{2}-54=0$$

Solve the quadratic equation by finding square roots or by using the quadratic formula. Explain why you chose the method. $$h^{2}+18 h+81=0$$

Solve the system of linear equations if possible. Does the system have exactly one solution, no solution, or infinitely many solutions? $$ \begin{aligned}&-2 x+2 y=4\\\&x-y=-2\end{aligned} $$

Use a table of values to graph the equation. $$y=3 x-1$$

Use the quadratic formula to solve the equation. $$2 x^{2}+4 x-3=0$$

In Exercises 67 and 68 , use the following information. On one of the banks of the Chicago River, there is a water cannon, called the Water Arc, that sprays recirculated water across the river. The path of the Water Arc is given by the model $$ y=-0.006 x^{2}+1.2 x+10 $$ where \(x\) is the distance (in feet) across the river, \(y\) is the height of the arc (in feet), and 10 is the number of feet the cannon is above the river. What is the maximum height of the water sprayed from the Water Arc?

Solve the equation or write no solution. Write the solutions as integers if possible. Otherwise write them as radical expressions. $$7 x^{2}-63=0$$

Solve the quadratic equation by finding square roots or by using the quadratic formula. Explain why you chose the method. $$5 x^{2}=25$$

Solve the system of linear equations if possible. Does the system have exactly one solution, no solution, or infinitely many solutions? $$ \begin{aligned}&8 x+4 y=-4\\\&4 x-y=-20\end{aligned} $$

In Exercises 67 and 68 , use the following information. On one of the banks of the Chicago River, there is a water cannon, called the Water Arc, that sprays recirculated water across the river. The path of the Water Arc is given by the model $$ y=-0.006 x^{2}+1.2 x+10 $$ where \(x\) is the distance (in feet) across the river, \(y\) is the height of the arc (in feet), and 10 is the number of feet the cannon is above the river. How far across the river does the water land?

Use a calculator to solve the equation or write no solution. Round the results to the nearest hundredth. $$4 x^{2}-3=57$$

Solve the quadratic equation by finding square roots or by using the quadratic formula. Explain why you chose the method. $$y^{2}-3 y=1$$

Solve the system of linear equations if possible. Does the system have exactly one solution, no solution, or infinitely many solutions? $$ \begin{aligned}&10 x-6 y=-5\\\&3 y=5 x+2\end{aligned} $$

In Exercises \(69-71\), use the following information. In Ghana from 1980 to \(1995,\) the annual production of gold \(G\) in thousands of ounces can be modeled by \(G=12 t^{2}-103 t+434,\) where \(t\) is the number of years since 1980 . From 1980 to \(1995,\) during which years was the production of gold in Ghana decreasing?

Use a calculator to solve the equation or write no solution. Round the results to the nearest hundredth. $$6 y^{2}+22=34$$

Solve the quadratic equation by finding square roots or by using the quadratic formula. Explain why you chose the method. $$v^{2}=8 v+2$$

Solve the system of linear equations if possible. Does the system have exactly one solution, no solution, or infinitely many solutions? $$ \begin{aligned}&4 y=-5 x-3\\\&15 x+12 y=9\end{aligned} $$

Simplify the expression. Then evaluate the expression when \(a=1\) and \(b=2\). $$\left(a^{3} b\right)^{4}$$

In Exercises \(69-71\), use the following information. In Ghana from 1980 to \(1995,\) the annual production of gold \(G\) in thousands of ounces can be modeled by \(G=12 t^{2}-103 t+434,\) where \(t\) is the number of years since 1980 . From 1980 to \(1995,\) during which years was the production of gold increasing?

Use a calculator to solve the equation or write no solution. Round the results to the nearest hundredth. $$2 x^{2}-4=10$$

Evaluate the expression to the nearest hundredth. $$ \frac{5 \pm 3 \sqrt{6}}{2} $$

Rewrite the expression using positive exponents. $$\frac{1}{2 x^{-5}}$$

Use a calculator to solve the equation or write no solution. Round the results to the nearest hundredth. $$\frac{2}{3} n^{2}-6=2$$

Evaluate the expression to the nearest hundredth. $$ \frac{2 \pm 6 \sqrt{3}}{3} $$

Rewrite the expression using positive exponents. $$\frac{1}{4 x^{-7}}$$

Evaluate the expression to the nearest hundredth. $$ \frac{-3 \pm 2 \sqrt{5}}{-1} $$

Rewrite the expression using positive exponents. $$x^{-4} y^{3}$$

TABLE TENNIS In Exercises \(72-75,\) use the following information. Suppose a table-tennis ball is hit in such a way that its path can be modeled by \(h=-4.9 t^{2}+2.07 t,\) where \(h\) is the height in meters above the table and \(t\) is the time in seconds. About how many seconds did it take for the table-tennis ball to reach its maximum height after its initial bounce? Round to the nearest tenth.

Use a calculator to solve the equation or write no solution. Round the results to the nearest hundredth. $$\frac{1}{2} x^{2}+3=8$$

Evaluate the expression to the nearest hundredth. $$ \frac{-2 \pm 4 \sqrt{2}}{-2} $$

Rewrite the expression using positive exponents. $$6 x^{-2} y^{-6}$$

Use a calculator to solve the equation or write no solution. Round the results to the nearest hundredth. $$3 x^{2}+7=31$$