Chapter 9

Solve the equation or write no real solution. Write the solutions as integers if possible. Otherwise, write them as radical expressions. $$ 7 x^{2}+30=9 $$

The variables \(x\) and \(y\) vary directly. Use the given values to write an equation that relates x and y .\( \text { (Lesson } 4.6)\) $$ x=14, y=7 $$

Sketch the graph of the function. Label the coordinates of the vertex. $$ y=-4 x^{2}+4 x+7 $$

Solve the equation algebraically. Check your solutions by graphing. $$2 x^{2}+8=16$$

Use the quadratic formula to solve the equation. If the solution involves radicals, round to the nearest hundredth. $$-3 y^{2}+2 y+8=0$$

Determine whether the graph of the function will intersect the x-axis in zero, one, or two points. \(y=3 x^{2}-6 x+3\)

Simplify the expression. $$ \sqrt{\frac{10}{162}} $$

Determine whether the number is a perfect square. $$ -5 $$

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

The variables \(x\) and \(y\) vary directly. Use the given values to write an equation that relates x and y .\( \text { (Lesson } 4.6)\) $$ x=-13, y=-52 $$

Sketch the graph of the function. Label the coordinates of the vertex. $$ y=-3 x^{2}-3 x+4 $$

Solve the equation algebraically. Check your solutions by graphing. $$3 x^{2}+5=32$$

Use the quadratic formula to solve the equation. If the solution involves radicals, round to the nearest hundredth. $$6 n^{2}-10 n+3=0$$

Simplify the expression. $$ \sqrt{\frac{12}{147}} $$

Determine whether the number is a perfect square. $$ 120 $$

Solve the equation or write no real solution. Write the solutions as integers if possible. Otherwise, write them as radical expressions. $$ 5 t^{2}+10=135 $$

The variables \(x\) and \(y\) vary directly. Use the given values to write an equation that relates x and y .\( \text { (Lesson } 4.6)\) $$ x=3, y=-6 $$

You throw a basketball. The height of the ball can be modeled by \(h=-16 t^{2}+15 t+6,\) where \(h\) represents the height of the basketball (in feet) and \(t\) represents time (in seconds). Find the vertex of the graph of the function. Interpret the result to find the maximum height that the basketball reaches.

Solve the equation algebraically. Check your solutions by graphing. $$2 x^{2}-7=11$$

Use the quadratic formula to solve the equation. If the solution involves radicals, round to the nearest hundredth. $$9 x^{2}+14 x+3=0$$

Determine whether the number is a perfect square. $$ 16 $$

Solve the equation or write no real solution. Write the solutions as integers if possible. Otherwise, write them as radical expressions. $$ 3 x^{2}-50=58 $$

The variables \(x\) and \(y\) vary directly. Use the given values to write an equation that relates x and y .\( \text { (Lesson } 4.6)\) $$ x=-5, y=60 $$

In Exercises 46 and 47 use the following information. A bottle-nosed 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 vertex of the parabola? Interpret the result.

Use the quadratic formula to solve the equation. If the solution involves radicals, round to the nearest hundredth. $$8 m^{2}+6 m-1=0$$

In Exercises 45 and 46, find and correct the error. $$ \frac{\sqrt{9}}{3}=3 $$

Determine whether the number is a perfect square. $$ 1 $$

Solve the equation or write no real solution. Write the solutions as integers if possible. Otherwise, write them as radical expressions. $$ m^{2}-12=52 $$

Graph the exponential function. (Lesson 8.3) $$ y=3^{x} $$

Use a graphing calculator to approximate the solutions of the equation. $$-x^{2}-3 x+4=0$$

Use the quadratic formula to solve the equation. If the solution involves radicals, round to the nearest hundredth. $$-\frac{1}{2} x^{2}+6 x+13=0$$

Use a graphing calculator and the following information. A software company’s net profit for each year from 1993 to 1998 lead a financial analyst to model the company’s net profit by $$P=6.84 t^{2}-3.76 t+9.29$$ where \(P\) is the profit in millions of dollars and \(t\) is the number of years since \(1993 .\) In 1993 the net profit was approximately 9.29 million dollars \((t=0)\). Give the domain and range of the function for 1993 through 1998.

Simplify the expression. $$ \sqrt{\frac{1}{5}} $$

Determine whether the number is a perfect square. $$ 111 $$

Solve the equation or write no real solution. Write the solutions as integers if possible. Otherwise, write them as radical expressions. $$ 2 y^{2}+13=41 $$

Graph the exponential function. (Lesson 8.3) $$ y=5^{x} $$

Natalya Lisovskaya holds the world record for the women's shot put. The path of her record-breaking throw can be modeled by \(h=-0.0137 x^{2}+0.9325 x+5.5,\) where \(h\) is the height (in feet) and \(x\) is the horizontal distance (in feet). Use a calculator to find the maximum height of the throw by Lisovskaya. Round to the nearest tenth.

Use a graphing calculator to approximate the solutions of the equation. $$ x^{2}+6 x-7=0 $$

Use the quadratic formula to solve the equation. If the solution involves radicals, round to the nearest hundredth. $$2 x^{2}-3 x+1=0$$

Use a graphing calculator and the following information. A software company’s net profit for each year from 1993 to 1998 lead a financial analyst to model the company’s net profit by $$P=6.84 t^{2}-3.76 t+9.29$$ where \(P\) is the profit in millions of dollars and \(t\) is the number of years since \(1993 .\) In 1993 the net profit was approximately 9.29 million dollars \((t=0)\). Use the graph to predict whether the net profit will reach 650 million dollars.

Simplify the expression. $$ \sqrt{\frac{5}{6}} $$

Determine whether the number is a perfect square. $$ 225 $$

Solve the equation or write no real solution. Write the solutions as integers if possible. Otherwise, write them as radical expressions. $$ 20-x^{2}=4 $$

Graph the exponential function. (Lesson 8.3) $$ y=3(2)^{x} $$

In Exercises \(49-51\), sketch the graphs of the three functions in the same coordinate plane. Then describe how the three parabolas are similar to each other and how they are different. $$ \begin{aligned} &y=-\frac{1}{2} x^{2}+x+1\\\ &y=-x^{2}+x+1\\\ &y=-2 x^{2}+x+1 \end{aligned} $$

Use a graphing calculator to approximate the solutions of the equation. $$-\frac{1}{2} x^{2}+2 x+16=0$$

Write the quadratic equation in standard form. Then solve using the quadratic formula. $$2 x^{2}=4 x+30$$

Use a graphing calculator and the following information. A software company’s net profit for each year from 1993 to 1998 lead a financial analyst to model the company’s net profit by $$P=6.84 t^{2}-3.76 t+9.29$$ where \(P\) is the profit in millions of dollars and \(t\) is the number of years since \(1993 .\) In 1993 the net profit was approximately 9.29 million dollars \((t=0)\). Use a graphing calculator to estimate how many years it will take for the company’s net profit to reach 475 million dollars according to the model.

Simplify the expression. $$ \sqrt{\frac{1}{2}} $$

Determine whether the number is a perfect square. $$ -4 $$