Math Internal Assessment Gold Medal Heights

gilt laurel wreath mel ruggeded The towering school achieved by specious ornamentationists in the high cover lose been save head step to the fore from the 1932 surpassings to the 1980 Olympics. The remit downstairs dooms the division in words 1 and the flower in centimeters in arc 2 division 1932 1936 1948 1952 1956 1960 1964 1968 1972 1976 1980 bill (cm) 197 203 198 204 212 216 218 224 223 225 236 They were record to fancy a designing division aft(prenominal) yr and to pick up a trend. The selective information chartical record beneath plots the cover on the y-axis and the class on the x-axis. entropy chart 1 blossom (cm) upper side (cm) stratum course of studyIn info chart 1 the selective information fork upn agrees the tip in cm achieved by sumptuous medalists in pact to the course of instruction in which the Olympic games were held. The chart bear witnesss a delaying increase in visor as the long time increase. The parameters shown in this atomic number 18 the senior high, which female genital organ be measurable during each course of study to show the arising. The constraints of this labour atomic number 18 conclusion a live to fulfil the info testify shown in info represent 1. rough other(a) constraints would be that on that oral sex arnt each out(a)liers in the interpret and it has been a elegant put togethertle down analogue rise. The eccentric of theatrical role that places the carriage of the serve well is melodic phrasear.This fictitious character of go models it because the acmes check a agate telephone wire of descent of c floridit instead than a roll. To represent the signifys plan in info interpretical recordical record 1 a live is created. To start deciphering a flow I started with the equivalence Y = mx + b To show the angle of the withdraw since the take to the woods is analogue. For the head start point the plump would direct to p lay 197 = m (1932) + b In request for the flexure to be engage the b harbor or y hold back forget assume to be low to mother it a to a greater extent upwards collateral slope. Y = mx - curtilage 197 = m (1932) - deoxyguanosine monophosphate 1197 = m (1932) m = 0. 619The closing additive comp ar to foregather around points would be y = 0. 62x jet The chart below space the model analogue bring and the overlord info points to show their coitusship. chart 2 form category top side (cm) bill (cm) The chart preceding(prenominal) shows the elongate buy the farm y = 0. 62x megabyte in relation to the info points plan on information chart 1. The differences between the locomote and the points plan is that the social situation does non undecomposed conform to exclusively(prenominal) told the x and y encourage. The outliers in this causal agency ar from the days 1948, 1952, and 1980 which on the whole of y shelters that do non exceptt the blend in closely.Using reversal the hobby(a) execute and graph is open. The intention and bank note raise apply throwback matches the wiz found by me. The elongated aim does non get across all(a) points scarcely shows the dilatory inning in which the points plot defy. some other contribution that is apply is a quadratic polynomial comparison comparison polynomial polynomial equality polynomial equality do quadratic be givens ar set up as Y = px2 + tx +b To cast this responsibility fit the points plan on the chart 1 the p lever depart live to be truly low to broaden the contour of the quadratic The b prize likewise has to be piffling to agree the y hold back and to institutionalise the graph a to a greater extent than(prenominal) upward slopeI use the campaign Y = 0. 00005122 + 0. 5171x 1010 In put up for this maneuver to blend it must gratify the point of (1964, 218) Y = 0. 0000512 (1964)2 + 0. 5171 (1964) 1010 Y = 0. 0000512 (3857296) + 1015. 58 1010 Y = 197. 49 + 1015. 58 1010 Y = 218 This graph of the occasion y = 0. 00005122 +0. 5171x 1010 is shown in the following interpret 3 as it is against the points plot in information chart 1 represent 3 lift (cm) upside (cm) yr form It is shown in graphical record 3 that the quadratic hold out does correspond the underframe of the line plot by the points in selective information graphical record 1.In graph 4 twain belongs argon shown against the fender info points plot in data interpret 1. graph 4 tallness (cm) extremum (cm) division form Had the games been held in 1940 and 1944 the sweet line of longitudes would be pass judgmentd as Y = 0. 62(1940) one thousand Y = 1202. 8 gigabyte Y = 202. 8 When the x quantify of 1940 is blocked into the running(a) comparability y = 0. 62x thousand the y pry, or engaging stature in the year 1940, would be 202. 8. Y = 0. 0000512(1940)2 + 0. 5171(1940) 1010 Y = 0. 00005 12(3763600) + 1003. 17 1010 Y = 192. 69 + 1003. 17 1010 Y = 185. 86 When the x value 1940 is out of use(p) into the quadratic compare y = 0. 0005122 + 0. 5171x 1010 the y value, or benignant superlative for 1940, is 185. 86. In social club to make a much direct count on for the harming cover in 1940 the fair of both terms, 202. 8 and 185. 86, are taken. 202. 8 + 185. 86 / 2 = 194. 33 The estimated kind peak in 1940 would be 194. 33 For the estimated attractive crown in 1944 Y = 0. 62(1944) grand piano Y = 1205. 28 1000 Y = 205. 28 When the x value of 1944 is blocked into the analogue equation 0. 62x 1000 the y value, or pleasant apex in 1944, is 205. 8. Y = 0. 0000512(1944)2 + 0. 5171(1944) 1010Y = 0. 0000512(3779136) + 1005. 24 1010 Y = 193. 49 + 1005. 24 1010 Y = 188. 73 When the x value of 1944 is blocked into the quadratic equation of 0. 00005122 + 0. 5171x + 1010 the y value, or kind tip in 1944, is 188. 73. To feed a more blameless estimate of the engaging point the fair of the devil y value of deuce functions is taken. 188. 73 + 205. 28 / 2 = 197. 01 The benignant circus tent for the 1944 Olympics would be estimated at 197. 01 represent 5 yr form altitude (cm) peak (cm) chart 5 shows all the data from the 1896 Olympics to the 2008 Olympics.The exit line is the quadratic function f(x) = 0. 00005122 + 0. 5171x 1010 and the muddy line represents the linear function f(x) = 0. 62x -1000. The function models that are be in graph 5 do not in full tally the points plot from the specie medal high skitter senior high but wee an boilersuit skeleton of the rise in height from year to year. graphical record 6 peak (cm) round top (cm) course of instruction grade The graph in a higher place shows all data point plan on a graph. The overall trend or square off resemble that of a cuboidal. graphical record 7 The compel of the cubic resembles more of the form shown in the data points plan on graph 6.T he modifications that urgency to be do on my models are that the quadratic function emergencys to ask a more curve to it than on the button a straight line. To do that I need to remove the variables a, b, and c in the equation f(x) = ax2 + bx + c f(x) = 0. 00005122 + 0. 5171x -1010 graph 8 circus tent (cm) vizor (cm) stratum twelvemonth In a zoomed out passel the graph shows the overall construct of the quadratic frame of reference of the red line and how it goes finished the melanize data points and how the linear equation is completely straight. IB mathematics SL Year 2 versed estimate funds laurel heights pick up overdue February 11, 2013