Name Date Chapter 0 Evaluate the expression. Fair Game Review. 9 +. + 6. 8 +. 9 00. ( 9 ) 6. 6 ( + ) 7. 6 6 8. 9 6 x 9. The number of visits to a website can be modeled b = +, where is hundreds of visits and x is the number of das since the website was launched. When did the website have 900 visits? Copright Big Ideas Learning, LLC Big Ideas Math Algebra 6
Name Date Chapter 0 Factor the polnomial. Fair Game Review (continued) 0. v v +. d + 9d + 8. k + k 6. m 0m. t t 90. f + 6f 7 6. a + 6a + 7. q q + 68 8. A swimming pool has a shallow end and a deep end. The total area (in square feet) of the swimming pool can be represented b x + 0x + 6. Write a binomial that represents the width w of the swimming pool. Shallow End Deep End w ft 8 ft x ft 6 Big Ideas Math Algebra Copright Big Ideas Learning, LLC
Name Date 0. Graphing Square Root Functions For use with Activit 0. Essential Question How can ou sketch the graph of a square root function? ACTIVITY: Graphing Square Root Functions Work with a partner. Make a table of values for the function. Use the table to sketch the graph of the function. Describe the domain of the function. Describe the range of the function. a. = x b. = x + 0 9 8 7 6 0 9 8 7 6 6 7 8 9 0 x 6 7 8 9 0 x Copright Big Ideas Learning, LLC Big Ideas Math Algebra 6
Name Date 0. Graphing Square Root Functions (continued) c. = x + d. = x 0 9 8 7 6 6 7 8 9 0 x 6 7 8 9 6 7 8 9 0 x ACTIVITY: Writing Square Root Functions Work with a partner. Write a square root function, = f( x), that has the given values. Then use the function to complete the table. a. b. f x x ( ) 0 0 x f( x ) 0 66 Big Ideas Math Algebra Copright Big Ideas Learning, LLC
Name Date 0. Graphing Square Root Functions (continued) ACTIVITY: Writing a Square Root Function Work with a partner. Write a square root function, = f( x), that has the given points on its graph. Explain how ou found our function. 6 7 8 9 0 x What Is Your Answer?. IN YOUR OWN WORDS How can ou sketch the graph of a square root function? Summarize a procedure for sketching the graph. Then use our procedure to sketch the graph of each function. a. = x b. = x c. = x d. = x Copright Big Ideas Learning, LLC Big Ideas Math Algebra 67
Name Date 0. Practice For use after Lesson 0. Find the domain of the function.. = x. = x. = x + Graph the function. Describe the domain and range. Compare the graph to the graph of = x.. = x. = x + O x O x 6. = x + 7. = x + + O x O x 8. The radius of a sphere is given b of the sphere. r S =, where S is the surface area π a. Find the domain of the function. Use a graphing calculator to graph the function. b. Use the trace feature to approximate the surface area of a sphere with a radius of centimeters. 68 Big Ideas Math Algebra Copright Big Ideas Learning, LLC
Name Date Extension 0. Simplif the expression. Practice For use after Extension 0.. 6.. 6. 8. 6. + 7 7 7. 8 + 8. 7 6 0 Copright Big Ideas Learning, LLC Big Ideas Math Algebra 69
Name Date Extension 0. Practice (continued) Simplif the expression. 9. 0. 6 +. 8. +. 9 + 8. 6. The distance d (in kilometers) that ou can see to the horizon with our ee level h meters above the water is given b d = h. How far can ou see when our ee level is meter above the water? m 70 Big Ideas Math Algebra Copright Big Ideas Learning, LLC
Name Date 0. Solving Square Root Equations For use with Activit 0. Essential Question How can ou solve an equation that contains square roots? ACTIVITY: Analzing a Free-Falling Object Work with a partner. The table shows the time t (in seconds) that it takes a free-falling object (with no air resistance) to fall d feet. a. Sketch the graph of t as a function of d. b. Use our graph to estimate the time it takes for a free-falling object to fall 0 feet. c. The relationship between d and t is given b the function t = d. 6 Use this function to check the estimate ou obtained from the graph. d feet t seconds 0 0.00. 6.00 96. 8.8 60.6 9.6.7 6.00 88. 0.7 d. Consider a free-falling object that takes seconds to hit the ground. How far did it fall? Explain our reasoning. 6 t 6 96 8 60 9 6 88 0 8 6 d Copright Big Ideas Learning, LLC Big Ideas Math Algebra 7
Name Date 0. Solving Square Root Equations (continued) ACTIVITY: Solving a Square Root Equation Work with a partner. Sketch the graph of each function. Then find the value of x such that f( x ) =. Explain our reasoning. a. f( x) = x b. f( x) = x 0 9 8 7 6 0 9 8 7 6 6 7 8 9 0 x 6 7 8 9 0 x ACTIVITY: Solving a Square Root Function Work with a partner. The speed s (in feet per second) of the free-falling object in Activit is given b the function s = 6 d. Find the distance traveled for each speed. a. s = 8 ft sec b. s = 6 ft sec c. s = ft sec 7 Big Ideas Math Algebra Copright Big Ideas Learning, LLC
Name Date 0. Solving Square Root Equations (continued) What Is Your Answer?. IN YOUR OWN WORDS How can ou solve an equation that contains square roots? Summarize a procedure for solving a square root equation. Then use our procedure to solve each equation. a. x + = b. x = c. = x + 0 d. = x Copright Big Ideas Learning, LLC Big Ideas Math Algebra 7
Name Date 0. Practice For use after Lesson 0. Solve the equation. Check our solution.. x + = 9. = 6 x. 7 = + x +. x =. x = x + 6 6. 8x + = 7x + 7 7. x = x 8. x + = x 9. The formula 8 S = df relates the speed S (in feet per second), drag factor f, and distance d (in feet) it takes for a car to come to a stop after the driver applies the brakes. A car travels at 80 feet per second and the drag factor is. What distance does it take for the car to stop once the driver applies the brakes? 7 Big Ideas Math Algebra Copright Big Ideas Learning, LLC
Name Date 0. The Pthagorean Theorem For use with Activit 0. Essential Question How are the lengths of the sides of a right triangle related? Pthagoras was a Greek mathematician and philosopher who discovered one of the most famous rules in mathematics. In mathematics, a rule is called a theorem. So, the rule that Pthagoras discovered is called the Pthagorean Theorem. Pthagoras (c. 70 B.C. c. 90 B.C.) ACTIVITY: Discovering the Pthagorean Theorem Work with a partner. a. On grid paper, draw an right triangle. Label the lengths of the two shorter sides (the legs) a and b. c b. Label the length of the longest side (the hpotenuse) c. c b a a c. Draw squares along each of the three sides. Label the areas of the three squares a, b, and c. b d. Cut out the three squares. Make eight copies of the right triangle and cut them out. Arrange the figures to form two identical larger squares. a e. What does this tell ou about the relationship among a, b, and c? c b Copright Big Ideas Learning, LLC Big Ideas Math Algebra 7
Name Date 0. The Pthagorean Theorem (continued) ACTIVITY: Finding the Length of the Hpotenuse Work with a partner. Use the result of Activit to find the length of the hpotenuse of each right triangle. a. b. 6 c c 8 c. d. c 0. c 0. 76 Big Ideas Math Algebra Copright Big Ideas Learning, LLC
Name Date 0. The Pthagorean Theorem (continued) ACTIVITY: Finding the Length of a Leg Work with a partner. Use the result of Activit to find the length of the leg of each right triangle. a. b. a. b What Is Your Answer?. IN YOUR OWN WORDS How are the lengths of the sides of a right triangle related? Give an example using whole numbers. Copright Big Ideas Learning, LLC Big Ideas Math Algebra 77
Name Date 0. Practice For use after Lesson 0. Find the missing length of the triangle... 8 ft c 8 m m ft b.. 7 a 6. cm.9 cm b. 6. a 8 d c 9 d 7. The figure shows the location of the eight ball and cue ball in a game of pool. How man inches from the bottom left corner pocket is the eight ball? in. in. 78 Big Ideas Math Algebra Copright Big Ideas Learning, LLC
Name Date 0. Using the Pthagorean Theorem For use with Activit 0. Essential Question In what other was can ou use the Pthagorean Theorem? The converse of a statement switches the hpothesis and the conclusion. Statement: If p, then q. Converse of the statement: If q, then p. ACTIVITY: Analzing Converses of Statements Work with a partner. Write the converse of the true statement. Determine whether the converse is true or false. If it is false, give a counterexample. a. If a = b a = b, then. Converse: b. If two nonvertical lines have the same slope, then the lines are parallel. Converse: c. If a sequence has a common difference, then it is an arithmetic sequence. Converse: d. If a and b are rational numbers, then a + b is a rational number. Converse: Is the converse of a true statement alwas true? alwas false? Explain. Copright Big Ideas Learning, LLC Big Ideas Math Algebra 79
Name Date 0. Using the Pthagorean Theorem (continued) ACTIVITY: The Converse of the Pthagorean Theorem Work with a partner. The converse of the Pthagorean Theorem states: If the equation a + b = c is true of the side lengths of a triangle, then the triangle is a right triangle. a. Do ou think the converse of the Pthagorean Theorem is true or false? How could ou use deductive reasoning to support our answer? b. Consider DEF with side lengths a, b, and c, such that a + b = c. Also consider JKL with leg lengths a and b, where K = 90. What does the Pthagorean Theorem tell ou about JKL? D a c E J b F What does this tell ou about c and x? a x What does this tell ou about DEF and JKL? K b L What does this tell ou about E? What can ou conclude? 80 Big Ideas Math Algebra Copright Big Ideas Learning, LLC
Name Date 0. Using the Pthagorean Theorem (continued) ACTIVITY: Developing the Distance Formula Work with a partner. Follow the steps below to write a formula that ou can use to find the distance between and two points in a coordinate plane. Step : Choose two points in the coordinate plane that do not lie on the same horizontal or vertical line. x, and x,. Label the points ( ) ( ) Step : Draw a line segment connecting the points. This will be the hpotenuse of a right triangle. x Step : Draw horizontal and vertical line segments from the points to form the legs of the right triangle. Step : Use the x-coordinates to write an expression for the length of the horizontal leg. Step : Use the -coordinates to write an expression for the length of the vertical leg. Step 6: Substitute the expressions for the lengths of the legs into the Pthagorean Theorem. Step 7: Solve the equation in Step 6 for the hpotenuse c. What does the length of the hpotenuse tell ou about the two points? What Is Your Answer?. IN YOUR OWN WORDS In what other was can ou use the Pthagorean Theorem?. What kind of real-life problems do ou think the converse of the Pthagorean Theorem can help ou solve? Copright Big Ideas Learning, LLC Big Ideas Math Algebra 8
Name Date 0. Practice For use after Lesson 0. Tell whether the triangle with the given side lengths is a right triangle... 6 mm d 0 d 0 mm mm 8 d. m,. m,.8 m. in., in., 6 in. Find the distance between the two points.. (, ), (, 6) 6. ( 6, ), (, ) 7. (, 7 ), (, ) 8. ( 9, ), (, 8) 9. The cross-section of a wheelchair ramp is shown. Does the ramp form a right triangle? in. in. in. 8 Big Ideas Math Algebra Copright Big Ideas Learning, LLC