Step 2: Find the coordinates of the vertex (h, k) Step 5: State the zeros and interpret what they mean. Step 6: Make sure you answered all questions.

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1 Chapter 4 No Problem Word Problems! Name: Algebra 2 Period: A. Solving from Standard Form 1. A ball is thrown so its height, h, in feet, is given by the equation h = 16t! + 10t where t is the time in seconds after it is thrown. Find the maximum height of the ball and find how long the ball is in the air. Step 1: Sketch a Picture Step 2: Find the coordinates of the vertex (h, k) Step 3: Give the vertex and tell what it means. Step 4: Use factoring, quadratic formula, or complete the square to find the zeros. Step 5: State the zeros and interpret what they mean. Step 6: Make sure you answered all questions. 2. While marching in a band, a drum major tosses a baton into the air and catches it. The height (in feet) of the baton after t seconds can be modeled by h = 16t! + 32t + 6. Find the maximum height of the baton. Determine how long the baton is in the air if the height at which the drum major catches it is 4 feet. 3. The height h(t) of a baseball t seconds after it is hit is given by the formula h t = 16t! + 48t + 2. Find the maximum height of the ball and when the baseball hits the ground.

2 B. Maximum or Minimum from Vertex Form 1. A suspension cable of a bridge can be modeled by the function y =!!""" x 1400! What is the least distance between the cable and the bridge itself? X is the horizontal distance and y is the vertical distance in feet. Step 1: Sketch a picture. Step 2: Find the coordinate of the vertex h, k Step 3: Explain what the coordinate of the vertex represent. Step 4: Find the zeros by square root method. Step 5: Explain what the zeros represent. Step 6: Interpret and answer all questions. 2. Flying fish use their pectoral fins like airplane wings to glide through the air. The path of the fish can be modeled by the quadratic function y =!!"#$ x 33! + 5. When does the fish reach its maximum height, what is the fish s maximum height, and how far can it fly before it reenters the water? 3. The arch of the Gateshead Millennium Bridge forms a parabola with the equation y = x 52.5! + 45 where x is the horizontal distance in meters from the arch s left end and y is the distance in meters from the base of the arch. What is the width of the arch?

3 C. Solving a problem in Intercept Form. 1. A path of a football can be modeled by the function y = 0.03x(x 52) where x is the horizontal distance (in yards) and y is the corresponding height (in yards). How far is the football kicked? What is the maximum height? Step 1: Sketch a picture Step 2: Find the intercepts; interpret what they mean. Step 3: Find the axis of symmetry halfway between the intercepts. Step 4: Find the maximum height of the axis. Step 5: Give the vertex and interpret what they mean. Step 6: Answer all questions 2. The flight of a golf shot can be modeled by the function y = 0.001x(x 260) where x is the horizontal distance in yards from the impact point and y is the height in yards. How many yards away from the impact point does the ball land and what is the maximum height of the golf shot? 3. The function h x = x(x 143.9) models the path of the water shot by a water cannon where x is the horizontal distance (in feet) and h(x) is the corresponding height (in feet). How far does the water shoot? What is the maximum height of the water?

4 D. Dropped Object 1. How long does it take a ball to fall from a height of 100 feet above the ground? Step 1: Sketch a picture. Step 2: Write the quadratic function using the model: h t = 16t! + h!. Step 3: Solve for time (t) in seconds. 2. A diver dives off a cliff 40 feet above the water. How long is the diver in the air? 3. An apple falls from a tree from a height of 36 feet. When does it hit the ground? 4. You are dropping a ball from a height of 29 feet above the ground and your sister catches it 4 feet above the ground. How long is the ball in the air before it is caught?

5 E. Projectile Motion 1. A baseball is hit with a velocity of 96 feet per second from a height of 3 feet. Find the maximum height of the ball and when it will hit the ground. Step 1: Sketch a picture Step 2: Write the quadratic function in the form: h(t) = 16t! + v! t + h! Step 3: Identify the vertex. Step 4: Give the vertex and explain what it means. Step 5: Set the equation equal to zero and solve for t. Explain what it means. 2. A basketball player passes the ball to a teammate. The ball leaves the player s hands 5 feet above the ground and has an initial velocity of 55 feet per second. The teammate catches the ball when it returns to a height of 5 feet. What is the maximum height of the ball and how long is the ball in the air? 3. Jess is standing on the edge of a foot cliff. He kicks a ball into the air with an upward velocity of 32 feet/second. What is the maximum height of the ball? When does the ball reach the maximum height? When is the ball back at its starting point? When does the ball hit the ground?

6 F. Maximizing Revenue or Yield 1. A paintball range has about 380 players per week and charges $35 to play. The owner estimates that there will be 20 more players per week for every $1 reduction in the price. How can the owner maximize weekly revenue? Step 1: Define the variables. Step 2: Write the verbal model. Step 3: Write a quadratic function. Step 4: Simplify the function. Step 5: Find the coordinates of the vertex (x, R(x)). Step 6: Give the vertex and tell what it means. Answer all questions. 2. An electronic store sells about 70 of a new model of digital cameras per month at $320 each. For each $20 decrease in price, about 5 more cameras per month are sold. How can the store maximize monthly revenue? 3. An online music store sells about 4000 songs each day when it charges $1 per song. For each $0.05 increase in price about 80 fewer songs per day are sold. How can the store maximize daily revenue?

7 G. Increasing Area, Finding New Dimensions 1. A park with a rectangular shape measures 600 meters by 400 meters. The park is to be doubled in size by adding the same distance to the length and width. Find the new dimensions. Step 1: Draw a picture and label dimensions. Step 2: Write a verbal model. Step 3: Write a quadratic function. Step 4: Simplify the function. Step 5: Factor and solve. Step 6: Give the new dimensions. 2. A deck is 21 feet by 20 feet. Its area is halved by subtracting the same distance, x, from the length and the width. Find x and give the new dimensions.