Chapter 9

Physicians can approximate the Body Surface Area of an adult (in square meters) using an index called \(B S A\) where \(H\) is height in centimeters and \(W\) is weight in kilograms. Body Surface Area: \(\sqrt{\frac{H W}{3600}}\) Find the \(B S A\) of a person who is 160 centimeters tall and weighs 50 kilograms.

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

Solve the equation or write no solution. Write the solutions as integers if possible. Otherwise write them as radical expressions. $$b^{2}=64$$

Find the x-intercepts of the graph of the equation. $$y=2 x^{2}-2 x-12$$

Use the following information. The number of recreational vehicles (RVs) sold in the United States from 1985 to 1991 can be modeled by \(N=-9.5 t^{2}+48.9 t+343.5,\) where \(N\) represents the number of vehicles sold (in thousands) and \(t\) represents the number of years since 1985. According to the model, in what year will the number of RVs sold in the United States drop to \(0 ?\)

The variables x and y vary directly. Use the given values to write an equation that relates x and y. $$x=4.6, y=1.2$$

A tsunami is a destructive, fast-moving ocean wave that is caused by an undersea earthquake, landslide, or volcano. The Pacific Tsunami Warning Center is responsible for monitoring earthquakes that could potentially cause tsunamis in the Pacific Ocean. Through measuring the water level and calculating the speed of a tsunami, scientists can predict arrival times of tsunamis. The speed \(s\) (in meters per second) at which a tsunami moves is determined by the depth \(d\) (in meters) of the ocean. \(s=\sqrt{g d},\) where \(g\) is 9.8 meters per second per second. Find the speed of a tsunami in a region of the ocean that is 1000 meters deep. Write the result in simplified form.

SKETCHING GRAPHS Sketch the graph of the function. Label the vertex. $$ y=3 x^{2}-2 x-1 $$

Solve the equation or write no solution. Write the solutions as integers if possible. Otherwise write them as radical expressions. $$5 x^{2}=500$$

Find the x-intercepts of the graph of the equation. $$y=-2 x^{2}+6 x+9$$

Sketch the graph of the exponential equation. $$y=2^{x}$$

A tsunami is a destructive, fast-moving ocean wave that is caused by an undersea earthquake, landslide, or volcano. The Pacific Tsunami Warning Center is responsible for monitoring earthquakes that could potentially cause tsunamis in the Pacific Ocean. Through measuring the water level and calculating the speed of a tsunami, scientists can predict arrival times of tsunamis. The speed \(s\) (in meters per second) at which a tsunami moves is determined by the depth \(d\) (in meters) of the ocean. \(s=\sqrt{g d},\) where \(g\) is 9.8 meters per second per second. Find the speed of a tsunami in a region of the ocean that is 4000 meters deep. Write the result in simplified form.

SKETCHING GRAPHS Sketch the graph of the function. Label the vertex. $$ y=2 x^{2}+6 x-5 $$

Solve the equation or write no solution. Write the solutions as integers if possible. Otherwise write them as radical expressions. $$x^{2}=16$$

Find the x-intercepts of the graph of the equation. $$y=x^{2}+x-4$$

What are the \(x\) -intercepts of \(y=x^{2}-2 x-3 ?\) \(\begin{array}{lllll}\text { (A) } 1 \text { and }-3 & \text { (B) }-2 \text { and }-3 & \text { (C) } 6 \text { and }-1 & \text { (D) } 3 \text { and }-1\end{array}\)

Sketch the graph of the exponential equation. $$y=0.5^{x}$$

SKETCHING GRAPHS Sketch the graph of the function. Label the vertex. $$ y=-3 x^{2}-2 x-1 $$

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

Find the x-intercepts of the graph of the equation. $$y=x^{2}+7 x-2$$

Sketch the graph of the exponential equation. $$y=\frac{1}{2}(2)^{x}$$

Which is the simplified form of \(4 \frac{\sqrt{125}}{\sqrt{25}} ?\) (A) \(2 \sqrt{5}\) (B) \(4 \sqrt{5}\) (C) \(20 \sqrt{5}\) (D) \(\frac{4 \sqrt{5}}{5}\)

SKETCHING GRAPHS Sketch the graph of the function. Label the vertex. $$ y=-4 x^{2}+32 x-20 $$

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

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. $$ 3 x^{2}+2 x+5=6 x^{2} $$

Find the x-intercepts of the graph of the equation. $$y=-3 x^{2}-2 x+1$$

Sketch the graph of the exponential equation. $$y=0.9^{x}$$

Which is the simplificd form of \(33 \sqrt{\frac{2}{121}} ?\) (A) \(\frac{2 \sqrt{33}}{\sqrt{11}}\) (B) \(33 \sqrt{2}\) (C) \(3 \sqrt{2}\) (D) \(\frac{3 \sqrt{2}}{\sqrt{11}}\)

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

Solve the equation or write no solution. Write the solutions as integers if possible. Otherwise write them as radical expressions. $$3 x^{2}=6$$

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. $$ -5 x^{2}+4 x=2 x^{2}-8 $$

Sketch the graph of the exponential equation. $$y=4(1.5)^{x}$$

Which is the simplificd form of \(\frac{6 \sqrt{52}}{\sqrt{2}} \cdot \sqrt{8}^{?}\) (A) \(\frac{3 \sqrt{13}}{\sqrt{2}}\) (B) \(3 \sqrt{13}\) (C) \(3 \sqrt{26}\) (D) \(\frac{6 \sqrt{13}}{\sqrt{2}}\)

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

Solve the equation or write no solution. Write the solutions as integers if possible. Otherwise write them as radical expressions. $$a^{2}+3=12$$

Find the x-intercepts of the graph of the equation. $$y=-5 x^{2}+5 x+5$$

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. $$ -2 x^{2}+5 x=8 x^{2}-2 $$

Sketch the graph of the exponential equation. $$y=5(0.5)^{x}$$

You can obtain a graphical representation of the relationship \(2^{1 / 2}=\sqrt{2}\) by investigating the graph of \(f(x)=2^{x}\) a. Graph \(f(x)=2^{x}\) b. Use the Trace feature to find values of \(f\) when \(x=\frac{1}{2}\) c. Compare the value from part (b) with the value of \(\sqrt{2}\).

SKETCHING GRAPHS Sketch the graph of the function. Label the vertex. $$ y=-2 x^{2}+6 x-5 $$

Solve the equation or write no solution. Write the solutions as integers if possible. Otherwise write them as radical expressions. $$x^{2}-7=57$$

Solve the quadratic equation by finding square roots or by using the quadratic formula. Explain why you chose the method. $$6 x^{2}+20 x+5=0$$

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. $$ -x^{2}-2=4 x^{2}+6 x-3 $$

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

Using the fact that \(x^{1 / 2}=\sqrt{x}\), rewrite in simplest radical form. $$6 x^{1 / 2}$$

SKETCHING GRAPHS Sketch the graph of the function. Label the vertex. $$ y=-\frac{1}{3} x^{2}+2 x-3 $$

Solve the equation or write no solution. Write the solutions as integers if possible. Otherwise write them as radical expressions. $$2 s^{2}-5=27$$

Solve the quadratic equation by finding square roots or by using the quadratic formula. Explain why you chose the method. $$m^{2}=32$$

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. $$ 0.75 x^{2}+2.67 x=6.22 x^{2}-4.1 $$

Use the quadratic formula to solve the equation. $$2 x^{2}-6 x+4=0$$