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Name: Block: Date: Unit 2 Exam Review352425028194000For each problem, identify the given features, create a graph, and describe the requested sections:fx=2x2+10x+8y-intercept: axis of symmetry:vertex:x-intercept(s):Graph it:Is the graph concave up or concave down?When is the graph increasing? When is the graph decreasing?When is the graph negative?What is the domain of the graph?What is the range of the graph?352996530543500gx=-(x-5)(x+1)x-intercept(s): axis of symmetry:vertex:y-intercept:Graph it:Is the graph concave up or concave down?When is the graph increasing? When is the graph decreasing?When is the graph positive?What is the domain of the graph?What is the range of the graph?3568065-3238500hx=-x-42+9vertex:axis of symmetry:x-intercept(s): y-intercept:Graph it:Is the graph concave up or concave down?When is the graph increasing? When is the graph decreasing?When is the graph negative?What is the domain of the graph?What is the range of the graph?3568065-3238500h(x)=0.5x+32vertex:axis of symmetry:x-intercept(s): y-intercept:Graph it:Is the graph concave up or concave down?When is the graph increasing? When is the graph decreasing?When is the graph negative?What is the domain of the graph?What is the range of the graph?Name: Block: Date: Exam review part 2: Practice with quadratic functions in contextA beginner pilot is participating in a flight simulation. In the simulation, the plane is in distress and losing altitude. The plane’s altitude can be modeled by the equation a(t) = 0.5(t – 11)2 + 1, where a(t) measures the altitude in feet and t is the number of seconds that have passed since the trouble was noticed. Will the plane crash? How do you know? a. No, the plane will not crash. The minimum height of the plane is 1 foot. b. No, the plane will not crash. The value of a is positive. c. Yes, the plane will crash. The minimum height is 11 feet. d. Yes, the plane will crash. The value of a is less than 1.A tourist jumps off a 16-foot cliff to swim with pink river dolphins in Bolivia. The tourist’s height in feet above the water is modeled by h(t) = –8t2+ 16t, where t is the time in seconds after the tourist jumps from the cliff. About how long will it take the tourist to reach the water? a. 2 seconds c. 1.5 seconds b. 0.5 seconds d. 1 second A local company manufactures custom truck parts for big rigs. The company’s average profit can be modeled by A(p) = –3(p)(p – 20), where A(p) is the average profit in dollars per p parts produced. What is a reasonable domain for this function? a. 0 to 10 parts c. 0 to 18 parts b. 0 to 14 parts d. 0 to 20 parts For the next two problems, determine whether the function has a minimum or maximum, identify the maximum or minimum, and identify the x and y intercepts. Identify what each of these features represents in context. Suppose the distance between a boomerang and the person who threw it follows a quadratic relationship in terms of the time t since it was thrown. The equation that models this situation is given by dt=-12t2+6t. The flight of a boulder launched from a catapult follows the quadratic equation H(x)= –x2+6x+16, where H(x) represents the height of the boulder in feet and x is the horizontal distance in feet the boulder travels after launch. A frog is about to hop from the bank of a creek. The path of the jump can be modeled by the equation h(x) = –x2 + 4x + 1, where h(x) is the frog’s height above the water and x is the number of seconds since the frog jumped. A fly is cruising at a height of 5 feet above the water. Is it possible for the frog to catch the fly, given the equation of the frog’s jump?It is Super Bowl season and teams that have made the play-offs have specialists evaluating every aspect of their field game. One particular team received news that their recently injured kicker’s field goal kick is modeled by the function h(t) = –16(t – 1) 2 + 16, where h(t) is the height of the ball in feet t seconds after it is kicked. If the football needs to clear a 17-foot goalpost, will the ball make it over if this particular team member kicks it?Reducing the cost of an item can result in a greater number of sales. You are trying to sell custom headphones and your business analysts have told you that the function that will predict your revenue in dollars, R(x), for each $1 change in price, x, for a set of headphones is R(x) = –100(x – 7)2 + 28,900. What is the maximum value of the function? What does the maximum value mean in the context of the problem? What price increase maximizes the revenue and what does it mean in the context of the problem? Shin is a beginner hang glider. He’s practicing jumping from a certain height, dipping initially, and then rising. Shin should dip to a height no lower than 6 feet above the ground, which is considered?a safe height, before changing direction and beginning to rise. The position of Shin’s hang glider is given by y = (x – 4)(x – 6), with x representing the time in seconds since Shin starts the initial jump and y representing the distance in feet from the safe height. Will Shin stay above the safe height? Why or why not? How long will it take for Shin to reach the initial height of the jump?Typically, cars achieve their best mileage when traveling at modest speeds. The gas mileage G(s) for a certain new car can be modeled by G(s)=-132s2+3s-39 when the speed, s, of the car in mph yields a mileage equal to or between 15 and 70 miles per gallon.At what values of s is the gas mileage decreasing?b. What is the car’s best gas mileage, and at what speed is it reached? ................
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