11.8 Basic applications of factoring 2016 ink.notebook. April 18, Page 144 Page Factoring Application Problems. Page 146.

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1 11.8 Basic applications of factoring 2016 ink.notebook Page 144 Page Factoring Application Problems Lesson Objectives Page 145 Standards Lesson Page Basic Applications of Factoring Press the tabs to view details. 1

2 Lesson Objectives Press the tabs to view details. Standards Lesson A.SSE.3 I will find the factors of a quadratic function and then solve to find the zeros A.APR.3 I will factor a quadratic function to determine the zeros A.REI.4 I will solve quadratic equations in height word problems F.IF.8 I will use factoring to find the zeros of a quadratic function Lesson Objectives Standards Lesson A.REI.4 Solve quadratic equations in one variable. b) Solve quadratic equations by inspection (e.g., for x 2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b. A.CED.2 Create equations in two or more variables to represent relationships between quantities; Graph equations on coordinate axes with labels and scales. A.SSE.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. a) Factor a quadratic expression to reveal the zeros of the function it defines. Press the tabs to view details. Round all answers to the nearest hundredth when necessary. 1. At a Fourth of July celebration, a rocket is launched straight up with an initial velocity of 125 feet per second. The height h of the rocket in feet above sea level is modeled by the formula h = 125t 16t 2, where t is the time in seconds after the rocket is launched. a) What is the height of the rocket when it returns to the ground? b) Let h = 0 in the equation and solve for t. c) How many seconds will it take for the rocket to return to the ground? 2

3 2. Jumping spiders can commonly be found in homes and barns throughout the United States. A jumping spider s jump can be modeled by the equation h = 33.3t 16t 2, where t represents the time in seconds and h is the height in feet. a) When is the spider s height at 0 feet? b) What is the spider s height after 1 second? after 2 seconds? 3. Penny is a Labrador Retriever who competes with her trainer in the agility course. Within the course, Penny must leap over a hurdle. Penny s jump can be modeled by the equation h = 16t t, where h is the height of the leap in inches at t seconds. Find the values of t when h = 0, by factoring first. 4. The height h in feet of an arrow can be modeled by the equation h = 64t 16t 2, where t is time in seconds. Ignoring the height of the archer, how long after the arrow is released does it hit the ground? 3

4 11.8 Basic applications of factoring 2016 ink.notebook 5. An arch decorated with balloons was used to decorate the gym for the spring dance. The shape of the arch can be modeled by the equation y = 0.5x x, where x and y are measured in feet and the x axis represents the floor. a) Write the expression that represents the height of the arch in factored form. b) How far apart are the two points where the arch touches the floor? 6. Sam is carpeting a room that has an area of x2 225 square feet. If the width of the room is x + 15 feet, what is the length? 4

5 11.8 Basic applications of factoring 2016 ink.notebook 7. The area of the rectangle below is 6x2 + 7x 3 square units. What is the width of the rectangle? 3x The length of a rectangle is 9 centimeters more than the width. The area of the rectangle is 22 square centimeters. What is the length? A = 22 cm2 x cm x + 9 cm 5

6 9. The area of a square is represented by 49x 2 126x Find the expression for the length of each side. 10. The sum of two numbers is 10. The product of the numbers is 24. Write a quadratic equation using this information. 11. Write a quadratic function in factored form that has zeros of 3 and 4. 6

7 On the Worksheet Practice Practice Practice Hint Round all answers to the nearest hundredth when necessary. 7

8 1. A ten inch fireworks shell is fired from ground level. The height of the shell in feet is given by the formula h = 263t 16t 2, where t is the time in seconds after the launch. a) Write the expression that represents the height in factored form. 2. A tennis player hits a tennis ball upward with an initial velocity of 80 feet per second. The height h in feet of the tennis ball can be modeled by the equation h = 80t 16t 2, where t is the time in seconds. Ignoring the height of the tennis player, how long does it take the ball to hit the ground? b) At what time will the height be 0? Is this answer practical? Explain. c) What is the height of the shell 8 seconds and 10 seconds after being fired? d) At 10 seconds, is the shell rising or falling? 3. When a ball is kicked in the air, its height in meters above the ground can be modeled by h(t) = 4.9t t where t is in seconds. How long was the ball in the air? 4. A firework s distance d meters from the ground is given by d = 1.5t t, where t is the number of seconds after the firework has been lit. How long is the firework in the air? 8

9 5. The area of the rectangle below is 2x 2 + 5x 12 square units. What is the width of the rectangle? 2x Sam is carpeting a room that has an area of x square feet. If the width of the room is x 14 feet, what is the length? a) x 14 ft b) x + 14 ft c) x 182 ft d) 14 ft a) x 4 b) x + 4 c) x 9 d) 2x The length of a rectangle is 7 centimeters more than the width. The area of the rectangle is 18 square centimeters. What is the length? 8. The area of a square is represented by 25x 2 80x Find the expression for the length of each side. A = 18 cm 2 x cm x + 7 cm 9

10 9. Luke is fertilizing a lawn that has an area of x x + 24 square feet. If the width of the lawn is x + 8 feet, what is the length? 10. The sum of two numbers is 13. The product of the numbers is 30. Write a quadratic equation using this information. 11. Write a quadratic function in factored form that has zeros of 2 and 6. Answers: 1a) t(16t 263) = 0 1b) t = 0 sec, t = sec. Yes the first one is the initial time to fire the shell. The second one is the time it takes to return to the ground. 1c) 1080ft, 1030ft 1d) falling t(t 3) = 0, t = 0, t = 3, 3 seconds 5. B 7. x 2 + 7x 18 = 0, (x + 9)(x 2) = 0, x = 9, x = 2, width = 2 cm, length = 9 cm 9. x y = (x 2)(x + 6) 10