Name Date Chapter Graph the linear equation. Fair Game Review. =. = +. =. =. = +. = + Copright Big Ideas Learning, LLC Big Ideas Math Algebra
Name Date Chapter Fair Game Review (continued) Evaluate the epression when =. 7. +. + + 9. 0. + 7 Evaluate the epression when =.. + +. + +. + 9.. The height (in feet) of a ball thrown off a balcon can be represented b t + t +, where t is time in seconds. a. Find the height of the ball when t =. b. The ball s velocit (in feet per second) can be modeled b = t +. Graph the linear equation. t Big Ideas Math Algebra Copright Big Ideas Learning, LLC
Name Date. Graphing = a For use with Activit. Essential Question What are the characteristics of the graph of the quadratic function = a? How does the value of a affect the graph of = a? ACTIVITY: Graphing a Quadratic Function Work with a partner. Complete the input-output table. Plot the points in the table. Sketch the graph b connecting the points with a smooth curve. What do ou notice about the graphs? a. = 0 0 9 7 b. = 0 7 9 0 Copright Big Ideas Learning, LLC Big Ideas Math Algebra
Name Date. Graphing = a (continued) ACTIVITY: Graphing a Quadratic Function Work with a partner. Graph each function. How does the value of a affect the graph of = a? a. = 0 9 7 = b. = = 0 Big Ideas Math Algebra Copright Big Ideas Learning, LLC
Name Date. Graphing = a (continued) c. = 0. = d. = 0 0 9 7 = What Is Your Answer?. IN YUR WN WRDS What are the characteristics of the graph of the quadratic function = a? How does the value of a affect the graph of = a? Consider a < 0, a >, and 0 < a < in our answer. Copright Big Ideas Learning, LLC Big Ideas Math Algebra
Name Date. Practice For use after Lesson. Graph the function. Compare the graph to the graph of. =. = =.. =. =. =. = 7 7. The path of a dolphin jumping out of water can be modeled b = 0.09, where and are measured in feet. Find the distance and maimum height of the jump. Big Ideas Math Algebra Copright Big Ideas Learning, LLC
Name Date. Focus of a Parabola For use with Activit. Essential Question Wh do satellite dishes and spotlight reflectors have parabolic shapes? ACTIVITY: A Propert of Satellite Dishes Work with a partner. Ras are coming straight down. When the hit the parabola, the reflect off at the same angle at which the entered. Draw the outgoing part of each ra so that it intersects the -ais. What do ou notice about where the reflected ras intersect the -ais? Where is the receiver for the satellite dish? Eplain. Ra Ra Ra = Incoming angle Copright Big Ideas Learning, LLC Big Ideas Math Algebra 7
Name Date. Focus of a Parabola (continued) ACTIVITY: A Propert of Spotlights Work with a partner. Beams of light are coming from the bulb in a spotlight. When the beams hit the parabola, the reflect off at the same angle at which the entered. Draw the outgoing part of each beam. What do the have in common? Eplain. = Beam Incoming angle Bulb Beam Beam Big Ideas Math Algebra Copright Big Ideas Learning, LLC
Name Date. Focus of a Parabola (continued) What Is Your Answer?. IN YUR WN WRDS Wh do satellite dishes and spotlight reflectors have parabolic shapes?. Design and draw a parabolic satellite dish. Label the dimensions of the dish. Label the receiver. Copright Big Ideas Learning, LLC Big Ideas Math Algebra 9
Name Date. Practice For use after Lesson. Graph the function. Identif the focus.. =. =. =. = Write an equation of the parabola with a verte at the origin and the given focus.. ( 0, ). ( 0, 0.) 7. A metal molding compan builds a solar furnace to power its factor. The furnace consists of hundreds of mirrors forming a parabolic dish that reflects the energ of the Sun to a focal point. Write an equation for the cross section of the dish when the receiver is feet from the verte of the parabola. 0 Big Ideas Math Algebra Copright Big Ideas Learning, LLC
Name Date. Graphing = a + c For use with Activit. Essential Question How does the value of c affect the graph of = a + c? ACTIVITY: Graphing = a + c Work with a partner. Sketch the graphs of both functions in the same coordinate plane. How does the value of c affect the graph of = a + c? a. = and = + 0 9 7 b. = and = 0 9 7 Copright Big Ideas Learning, LLC Big Ideas Math Algebra
Name Date. Graphing = a + c (continued) c. = + and = + 9 d. = = and 0 9 7 7 ACTIVITY: Finding -Intercepts of Graphs Work with a partner. Graph each function. Find the -intercepts of the graph. Eplain how ou found the -intercepts. a. = b. = 7 7 Big Ideas Math Algebra Copright Big Ideas Learning, LLC
Name Date. Graphing = a + c (continued) c. = + d. = 7 7 What Is Your Answer?. IN YUR WN WRDS How does the value of c affect the graph of = a + c? Use a graphing calculator to verif our conclusions. Copright Big Ideas Learning, LLC Big Ideas Math Algebra
Name Date. Practice For use after Lesson. Graph the function. Compare the graph to the graph of =.. =. = +. = = +. Describe how to translate the graph of given function. = to the graph of the. = +. = 7 7. A rock is dropped from a height of feet. The function h = + gives the height h of the rock after seconds. When does it hit the ground? Big Ideas Math Algebra Copright Big Ideas Learning, LLC
Name Date. Graphing = a + b + c For use with Activit. Essential Question How can ou find the verte of the graph of = a + b + c? ACTIVITY: Comparing Two Graphs Work with a partner. Sketch the graphs of = and = +. = = + 9 7 9 7 7 9 7 9 What do ou notice about the -value of the verte of each graph? Copright Big Ideas Learning, LLC Big Ideas Math Algebra
Name Date. Graphing = a + b + c (continued) ACTIVITY: Comparing -Intercepts with the Verte Work with a partner. Use the graph in Activit to find the -intercepts of the graph of =. Verif our answer b solving 0 =. Compare the location of the verte to the location of the -intercepts. ACTIVITY: Finding Intercepts Work with a partner. Solve 0 = a + b b factoring. What are the -intercepts of the graph of = a + b? Complete the table to verif our answer. = a + b 0 b a Big Ideas Math Algebra Copright Big Ideas Learning, LLC
Name Date.. Graphing = a + b + c (continued) ACTIVITY: Deductive Reasoning Work with a partner. Complete the following logical argument. b The -intercepts of the graph of = a + b are 0 and. a The verte of the graph of = a + b occurs when =. The vertices of the graphs of = a + b and = a + b + c have the same -value. The verte of = a + b + c occurs when =. What Is Your Answer?. IN YUR WN WRDS How can ou find the verte of the graph of = a + b + c?. Without graphing, find the verte of the graph of = +. Check our result b graphing. Copright Big Ideas Learning, LLC Big Ideas Math Algebra 7
Name Date. Practice For use after Lesson. Find (a) the ais of smmetr and (b) the verte of the graph of the function.. = +. = Graph the function. Describe the domain and range.. = +. = + + Tell whether the function has a minimum or a maimum value. Then find the value.. = +. = 0 + 9 7. The entrance of a tunnel can be modeled b = +, where and are measured in feet. What is the height of the tunnel? 0 Big Ideas Math Algebra Copright Big Ideas Learning, LLC
Name Date Etension. Practice For use after Etension. Graph the function. Compare the graph to the graph of = graphing calculator to check our answer.. = ( ). = ( + ). Use a. = ( + 7). = (.). = ( + ) +. ( ) = + Copright Big Ideas Learning, LLC Big Ideas Math Algebra 9
Name Date Etension. Practice (continued) 7. = ( + ). ( ) = = + 9. = ( ) + 0. ( ) Describe how the graph of g() compares to the graph of f().. g ( ) = f( 9). g ( ) f( ) = +. The profit (in millions) of compan A can be modeled b A = t + 0 and the profit (in millions) of compan B ( ) can be modeled b ( ) B = t + 9, where t is time in ears. a. How much greater is compan A s maimum profit than compan B s maimum profit? b. How man ears after compan A reached its maimum profit did compan B reach its maimum profit? 0 Big Ideas Math Algebra Copright Big Ideas Learning, LLC
Name Date. Comparing Linear, Eponential, and Quadratic Functions For use with Activit. Essential Question How can ou compare the growth rates of linear, eponential, and quadratic functions? ACTIVITY: Comparing Speeds Work with a partner. Three cars start traveling at the same time. The distance traveled in t minutes is miles. Complete each table and sketch all three graphs in the same coordinate plane. t = t t = t t = t 0 0 0 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0..0.0.0.0 Distance (miles) 0. 0. 0. 0. 0 0 0. 0. 0. 0. Time (minutes).0 t Copright Big Ideas Learning, LLC Big Ideas Math Algebra
Name Date. Comparing Linear, Eponential, and Quadratic Functions (continued) Compare the speeds of the three cars. Which car has a constant speed? Which car is accelerating the most? Eplain our reasoning. ACTIVITY: Comparing Speeds Work with a partner. Analze the speeds of the three cars over the given time periods. The distance traveled t minutes is miles. Which car eventuall overtakes the others? a. t = t t = t t = t Big Ideas Math Algebra Copright Big Ideas Learning, LLC
Name Date. Comparing Linear, Eponential, and Quadratic Functions (continued) b. t = t t = t t = t 7 7 7 9 9 9 What Is Your Answer?. IN YUR WN WRDS How can ou compare the growth rates of linear, eponential, and quadratic functions? Which tpe of growth eventuall leaves the other two in the dust? Eplain our reasoning. Copright Big Ideas Learning, LLC Big Ideas Math Algebra
Name Date. Practice For use after Lesson. Plot the points. Tell whether the points represent a linear, an eponential, or a quadratic function. 9.,,,, (, ), ( 0, ), (, 9). ( 0, ), (, ), (, ), (, ), (, ) Tell whether the table of values represents a linear, an eponential, or a quadratic function... 0 0 0. 0. Tell whether the data values represent a linear, an eponential, or a quadratic function. Then write an equation for the function using the form = m + b, = ab = a,or.. (, ), (, 7 ), (, ), ( 0, ), (, ). (, 0. ), ( 0, ), (, ), (, ), (, ) 7. The table shows the shipping cost c (in dollars) b weight w (in pounds) for items from an online store. a. Does a linear, an eponential, or a quadratic function represent this situation? Weight, w Cost, c.. b. How much does it cost to ship a -pound item? Big Ideas Math Algebra Copright Big Ideas Learning, LLC
Name Date Etension. Comparing Graphs of Functions For use with Etension. You have alread learned that the average rate of change (or slope) between an two points on a line is the change in divided b the change in. You can find the average rate of change between two points of a nonlinear function using the same method. ACTIVITY: Rates of Change of a Quadratic Function In Eample on page of our tetbook, the function f() t = t + 0t + gives the height (in feet) of a water balloon t seconds after it is launched. a. Complete the table for f (). t t 0 0..... f() t b. Graph the ordered pairs from part (a). Then draw a smooth curve through the points. c. For what values is the function increasing? 0 0 90 7 0 0 For what values is the function decreasing? t d. Complete the tables to find the average rate of change for each interval. Time Interval 0 to 0. sec 0. to sec to. sec. to sec to. sec Average Rate of Change (ft/sec) Time Interval. to sec to. sec. to sec to. sec. to sec Average Rate of Change (ft/sec) Copright Big Ideas Learning, LLC Big Ideas Math Algebra
Name Date Etension. Comparing Graphs of Functions (continued) Practice. Compared to the average rate of change of a linear function, what do ou notice about the average rate of change in part (d) of Activit?. Is the average rate of change increasing or decreasing from 0 to. seconds? How can ou use the graph to justif our answer?. What do ou notice about the average rate of change when the function is increasing and when the function is decreasing?. In Eample on page 9 of our tetbook, the function f( t) = t + gives the height of an egg t seconds after it is dropped. a. Complete the table for f (). t t 0 0.. f() t b. Graph the ordered pairs and draw a smooth curve through the points. c. Describe where the function is increasing and decreasing. 0 0..0. t d. Find the average rate of change for each interval in the table. What do ou notice? Big Ideas Math Algebra Copright Big Ideas Learning, LLC
Name Date Etension. Comparing Graphs of Functions (continued) ACTIVITY: Rates of Change of Different Functions The graphs show the number of videos on three video-sharing websites hours after the websites are launched. Linear Quadratic Eponential Number of videos 0 Website (, ) (, 0) (, ) (, ) (, ) (, ) (0, 0) 0 0 Time (hours) Number of videos 0 0 0 00 0 Website (, ) (, 00) 0 (, ) (, ) 0 (0, 0) (, ) 0 (, ) 0 0 Time (hours) Number of videos Website (, 09) 000 00 000 00 (, 0) 000 (0, ) 00 (, ) 000 (, ) (, ) 00 (, ) 0 0 Time (hours) a. Do the three websites ever have the same number of videos? b. Complete the table for each function. Linear Time Interval 0 to h to h to h to h to h to h Average Rate of Change (videos/hour) Quadratic Time Interval 0 to h to h to h to h to h to h Average Rate of Change (videos/hour) Eponential Time Interval 0 to h to h to h to h to h to h Average Rate of Change (videos/hour) Copright Big Ideas Learning, LLC Big Ideas Math Algebra 7
Name Date Etension. Comparing Graphs of Functions (continued) c. What do ou notice about the average rate of change of the linear function? d. What do ou notice about the average rate of change of the quadratic function? e. What do ou notice about the average rate of change of the eponential function? f. Which average rate of change increases more quickl, the quadratic function or the eponential function? Practice. REASNING How does a quantit that is increasing eponentiall compare to a quantit that is increasing linearl or quadraticall?. REASNING Eplain wh the average rate of change of a linear function is constant and the average rate of change of a quadratic or eponential function is not constant. Big Ideas Math Algebra Copright Big Ideas Learning, LLC