Chapter 12

Find the domain and the range of the function. Then sketch the graph of the function. $$y=\sqrt{2 x+5}$$

Find the x-intercepts of the graph of the equation. $$y=x^{2}+2 x+15$$

Solve the quadratic equation. $$4 x^{2}-2 x-1=0$$

Choose a method to solve the quadratic equation. Explain your choice. $$x^{2}+6 x-55=0$$

Use a graphing calculator to graphically solve the radical equation. Check the solution algebraically. $$\sqrt{x+4}=3$$

Use the following information. A trapezoid is isosceles if its two opposite nonparallel sides have the same length. Draw the polygon whose vertices are \(A(1,1), B(5,9), C(2,8),\) and \(D(0,4)\)

Find the domain and the range of the function. Then sketch the graph of the function. $$y=x \sqrt{8 x}$$

Find the x-intercepts of the graph of the equation. $$y=x^{2}+8 x+12$$

Solve the quadratic equation. $$x^{2}-6 x-1=0$$

Solve the quadratic equation. $$x^{2}-10 x=0$$

Use a graphing calculator to graphically solve the radical equation. Check the solution algebraically. $$\sqrt{x-5.6}=2.5$$

Find the x-intercepts of the graph of the equation. $$y=x^{2}+x-10$$

Solve the quadratic equation. $$a^{2}-6 a-13=0$$

Solve the quadratic equation. $$c^{2}+2 c-26=0$$

Use a graphing calculator to graphically solve the radical equation. Check the solution algebraically. $$\sqrt{9.2-x}=1.8$$

The period \(T\) (in seconds) of a pendulum is the time it takes for the pendulum to swing back and forth. The period is related to the length \(L\) (in inches) of the pendulum by the model \(T=2 \pi \sqrt{\frac{L}{384}} .\) Find the length of a pendulum with a period of eight seconds. Give your answer to the nearest tenth.

Find the x-intercepts of the graph of the equation. $$y=x^{2}+8 x+16$$

POLE-VAULTING A pole-vaulter's approach velocity \(v\) (in feet per 19 second) and height reached \(h\) (in feet) are related by the following equation. Pole-vaulter model: \(v=8 \sqrt{h}\) If you are a pole-vaulter and reach a height of 20 feet and your opponent reaches a height of 16 feet, approximately how much faster were you running than your opponent? Round your answer to the nearest hundredth.

Solve the quadratic equation. $$8 x^{2}+14 x=-5$$

Use a graphing calculator to graphically solve the radical equation. Check the solution algebraically. $$\sqrt{6 x-2}-3=7$$

What is the distance between \((-6,-2)\) and \((2,4) ?\) (A) \(2 \sqrt{5}\) (B) \(2 \sqrt{7}\) (C) 10 (D) 28

P. BioLoGY Many birds drop clams or other shellfish in order to break the shell and get the food inside. The time \(t\) (in seconds) it takes for an object such as a clam to fall a certain distance \(d\) (in feet) is given by the equation $$ t=\frac{\sqrt{d}}{4} $$ A gull drops a clam from a height of 50 feet. A second gull drops a clam from a height of 32 feet. Find the difference in the times that it takes for the clams to reach the ground. Round your answer to the nearest hundredth.

The lateral surface area \(S\) of a cone with a radius of 14 centimeters can be found using the formula $$S=\pi \cdot 14 \sqrt{14^{2}+h^{2}}$$ where \(h\) is the height (in centimeters) of the cone. a. Use unit analysis to check the units of the formula. b. Sketch the graph of the formula. c. Find the lateral surface area of a cone with a height of 30 centimeters.

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

Solve the quadratic equation. $$x^{2}-16=0$$

Use a graphing calculator to graphically solve the radical equation. Check the solution algebraically. $$4+\sqrt{x}=9$$

What is the midpoint between \((-2,-3)\) and \(\left(1, \frac{1}{2}\right) ?\) \(\begin{array}{llll}\text { (A) }\left(-1,-2 \frac{1}{2}\right) & \text { (B }\left(-\frac{1}{2},-2 \frac{1}{2}\right) & \text { C }\left(-1,-1 \frac{1}{4}\right) & \text { \odot }\left(-\frac{1}{2},-1 \frac{1}{4}\right)\end{array}\)

The average speed of an object \(S\) (in feet per second) that is dropped a certain distance \(d\) (in feet) is given by the following equation. Falling object model: \(S=\frac{d}{\frac{\sqrt{d}}{4}}\) Rewrite the equation with the right-hand side in simplest form.

An accident reconstructionist is responsible for finding how fast cars were going before an accident. To do this, a reconstructionist uses the model below where \(S\) is the speed of the car in miles per hour, \(d\) is the length of the tires' skid marks in feet, and \(f\) is the coefficient of friction for the road. Car speed model: \(S=\sqrt{30 d f}\) a. In an accident, a car makes skid marks 74 feet long. The coefficient of friction is \(0.5 .\) A witness says that the driver was traveling faster than the speed limit of 45 miles per hour. Can the witness's statement be correct? Explain your reasoning. b. How long would the skid marks have to be in order to know that the car was traveling faster than 45 miles per hour?

Find the x-intercepts of the graph of the equation. $$y=x^{2}-8 x-11$$

Solve the quadratic equation. $$x^{2}+12 x+20=0$$

Use a graphing calculator to graphically solve the radical equation. Check the solution algebraically. $$\sqrt{7 x-12}=x$$

The vertices of a right triangle are \((0,0),(0,6),\) and (6, 0). What is the length of the hypotenuse? (A) 6 B) \(6 \sqrt{2}\) (C) 36 (D) 72

Use the following information. The average speed of an object \(S\) (in feet per second) that is dropped a certain distance \(d\) (in feet) is given by the following equation. Falling object model: \(S=\frac{d}{\frac{\sqrt{d}}{4}}\) Use either equation to find the average speed of an object that is dropped from a height of 400 feet.

Find the x-intercepts of the graph of the equation. $$y=x^{2}+8 x-10$$

Solve the quadratic equation. $$x^{2}-4 x=\frac{5}{6}$$

Use a graphing calculator to graphically solve the radical equation. Check the solution algebraically. $$\sqrt{2 x+7}=x+2$$

Find the x-intercepts of the graph of the equation. $$y=3 x^{2}+20 x+1$$

Solve the quadratic equation. $$4 x^{2}+4 x+1=0$$

Use a graphing calculator to graphically solve the radical equation. Check the solution algebraically. $$\sqrt{3 x-2}=4-x$$

$$\text { Simplify } \sqrt{5}(6+\sqrt{5})^{2}$$ $$\begin{array}{llllll} \text { (A) } 41+2 \sqrt{5} & \text { (B) } 53 \sqrt{5} & \text { (C) } 41 \sqrt{5}+60 & \text { (D } 101 \sqrt{5} \end{array}$$

The relationship between a roller coaster's velocity \(v(\text { in feet per second })\) at the bottom of a drop and the height of the drop \(h\) (in feet) can be modeled by the formula \(v=\sqrt{2 g h}\) where \(g\) represents acceleration due to gravity. a. Use the fact that \(g=32 \mathrm{ft} / \mathrm{sec}^{2}\) to show that \(v=\sqrt{2 g h}\) can be simplified to \(v=8 \sqrt{h}\) b. Sketch the graph of \(v=8 \sqrt{h}\) c. Writing Use the formula or the graph to explain why doubling the height of a drop does not double the velocity of a roller coaster.

Find the x-intercepts of the graph of the equation. $$y=-x^{2}+4 x+1$$

Solve the quadratic equation. $$13 x^{2}-26 x=0$$

Use a graphing calculator to graphically solve the radical equation. Check the solution algebraically. $$\sqrt{15-4 x}=2 x$$

Which of the following is the difference \(\sqrt{3}-5 \sqrt{9} ?\) $$\begin{aligned} &\begin{array}{llll} \text { A) } \sqrt{3}-3 & \text { (B) } \sqrt{3}-15 & \text { (C) }-4 \sqrt{3} \end{array}\\\ &\text { (D) } \sqrt{3}-45 \end{aligned}$$

Find the domain of \(y=\frac{3}{\sqrt{x}-2}\)

Factor the expression. $$x^{2}-64$$

Solve the quadratic equation. $$4 p^{2}-12 p+5=0$$

Factor the expression completely. \(3 x^{3}+12 x^{2}-15 x\)