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# 3.5 Applications of Quadratic Functions 1130-02

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This 4 page Class Notes was uploaded by Kiana Thompson on Sunday October 4, 2015. The Class Notes belongs to 1130-02 at University of Tennessee - Chattanooga taught by John Graef in Summer 2015. Since its upload, it has received 24 views. For similar materials see College Algebra in Math at University of Tennessee - Chattanooga.

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Date Created: 10/04/15

35 Applications of Quadratic Equations EX 1 If an object is thrown upward with an initial velocity of 80 ft second then its height after t seconds is given by h 80t 16t2 a Find the maximum height obtained by the object b h b Find the vertex Z a 80 amp SW 2 2 2 16 32 32 84 2 h 2 2 5 2 5 80 2 16 405 1625 200 100 100 Maximum Height 100 ft b Find the number of seconds it takes the object to hit the ground Factor 0 80t 16t2 Ot80 16t O 16t 5 t 16t O amp 5 t O t 0 amp t 5 EX 2 Carol Bey makes and sells candy She has found that the cost per box for making x boxes of candy is given by Cx x2 40x 405 a How much does it cost per box to make 15 boxes 18 boxes 30 boxes Plug in 15 18 amp 30 for x then divide by Cx C15 152 4015 405 C15 30 C15 3015 2 2 per box for 15 boxes C18 182 4018 405 C18 9 C18 918 5 I 050 per box for 18 boxes C30 302 4030 405 C30 105 C30 10530 35 350 per box for 30 boxes b Graph the cost function Cx and mark the points corresponding to 15 18 and 30 boxes dinU 5 32 24 16 c What point on the graph Will make the cost per box as small as possible The Vertex would be the point used 1 How many boxes should she make in order to keep the cost per box at a minimum What is the minimum cost per box Find vertex Vertex 20 5 20 boxes 5 per box minimum amount needed EX 3 A researcher is physiology has decided that a good mathematical model for the number of impulses fired after a nerve has been stimulated is given by y x2 20x 60 Where y is the number of responses per millisecond and x is the number of milliseconds since the nerve was stimulated a When Will the maximum firing rate be reached Find the vertex y x2 20x 6O 20 20 y 2 1 7 10 y 102 2010 60 y 40 VERTEX 10 40 maximum ring rate reached b What is the maximum firing rate Maximum firing rate Will be the y from the vertex MAXIMUM FIRING RATE 40 EX 4 Find the break even point Rx 200x x2 Cx 70x 2200 O S x S 100 Set both equal to each other 200X X2 70X 2200 Simp1ify and set equal to zero 0 X2 130X 2200 Factor X213OX42200 Xx20X110 Set both equal to zero X 20 0 amp X 110 0 x20 amp x1H Since X i be greater than 100 your answer is X20

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