Solving Quadratics with Calculator

Algebra II (Application: Day 1) U3 L5 WS: Solving Quadratics w/ Calculator Name Solve each quadratic by graphing on the calculator. Find the zeroes (solutions) and the maximum or minimum valuc. Round all answers to the nearest hundredth, unless indicated otherwise. 1) f(x) = -14x* -17x + 50 4,2 + 44x-15=0 umax: 55. 1001 1200% 3) -1772+1.5x+55 = -3x -5 - 2.512, 1,318 change min 318 134 + 5 -17×7+4•5*+ 60=0 -33.085 .33' umax 60,29; -1175, 2,015 4) Randall Curtain High School's changing enrollment, E, for 1955 to 1975 can be modeled by the cquation E = 0.3712 -14.81 + 460. (Round each answer to the nearest whole number.) a) If 1950 is represented by ( - 0, in what year was the enrollment at a minimum? 1910 20 us later b) What was the minimum enrollment? 1950+20 = 1910 312. 5) In 1970, Harris Teeter opened a grocery store in your neighborhood. For the next /wenty yeary, annual sales, S (in millions of dollars), can be modeled by the equation S = -0.0151? +36r + 0.5 where / = 0 represents 1970. max a) During which year did they make thems rony?. 1982, 1910+72. b) What was the maximum in annual sales? 2.coco mullenni 6) A ball is thrown straight upward from the ground level with an initial velocity of 32 feet per second. The formula h(0) = 321-16r gives its height, h, after 1 seconds. a) What is the maximum height reached by the ball? Ile feet b) When does the ball hit the ground? 2 sec 7) The function f(x) = -0.019x* + 3.04x - 58.87 describes newspaper circulation (in millions) in the United States for the ycars 1920 to 1998 (x = 20 for 1920). Identify periods of increasing and decreasing circulation. a) According to the function, when did newspaper circulation peak? 1980 b) When will circulation reach 45 million? 19.49, 2010 find x 2104 Uner lied 8) The height of a baseball, just hit, is approximated by h(x) = -0.0011x? +0.4545x + 3 where x is 147. the horizontal distance from homeplate. The ball is approaching the ten-foot outfield wall, 400 feet from homeplate. If the ball is not caught, will it go over the wall? no because 01400ft, tubalwne lie cuẩi the kay. 400 x max 200 Quadratic Applications 1. Miranda throws a set of keys up to her brother, who is standing on a third-story balcony with his hands 38 feet above the ground. If Miranda throws the key with an initial velocity of 40 feet per second, the equation h = -16t' + 40t + $ gives the height h of the keys after t seconds. a) How long does it take the keys to reach their highest point?_ 1.2.5 sec b) How high do the keys reach? 3C. jat e) Will her brother be able to catch the keys, why or why no? no, Keys... 2. A stone was thrown from the top of a cliff 60 meters above sea level. The height H metres, of the stone above sea level t seconds after it was released is given by 1) = -5/7 + 20г + 60. a) Find the time taken for the stone to reach its maximum height. _ b) What is the maximum height above sea level reached by the stone? _ 80 meters. c) How long is it before the stone strikes the water? o c: C 3. The height H metres of a cannonball t seconds after it is fired into the air is given by H(1) = -4г* + 167 +9 a) Find the time taken for the cannonball to reach its maximum height. 2 sec b) What is the maximum height reached by the cannonball? 2.51t c) How long does it take for the cannonball to fall back to earth?. 4.5 300 4. The height of a punted football can be modeled with the quadratic function h(x) = -01x? +1.18x + 2. The horizontal distance in feet form the point of impact with the kicker's foot is x, and h is the height of the ball in feet. a) What is the maximum height of the punt? 36.81-5126 b) c) Tith mast defensively is block tie pull to ma Serid x: 5) high must the player reach to block the punt? field would the ball go before it hit the ground? 5. A projectile is fired from a clift 200 feet above the water at an inclination of 45° to the horizontal, with a muzzle velocity of 50 feet per second. The height h of the projectile is given by h(x) + - 32х*) - x + 200. (50)* a) b) How fy from the base of the dil is the height of the projictil a maximum? Find the maximum height of the projectile. 21100: When the height of the projectile is 100 feet above the water, how far is it from the clift? 35410