University:
High School
Course:
High School Functions
Academic year:

2024
Views:

12

Pages:

4
Author:

J. Anderson

1.3 Max or Min of a Quadratic Function - WorksheetMCR3USOLUTIONSlensen1) Determine the vertex for each quadratic function by completing the square. State if the vertex is amaximum or a minimum.) ((x) = x 2 + 14x - 14(x2+14x)-14(x2-6x)+17=(x3-6x+9-9)+17(x-6x+9)-9H7( x (3)' +8(x+7)2.63vestex is (-7,-63) and is a minimumvertex (3,8) and a minimumd)f(x) = 2x2 + 12x + 16: (2x21-12x)+162(x2+6x+9-9)+162(x2++6x+9)-18+16(x+7)---2(x+3)vertex is (3, ) is a minimumvotex is (-3,-2) and is a minimume)f(x)=-3x2+6x+1= (-3x2 (6x)+)+3(x2-2xt1)+3+1:- 3 (x-1)' +4Vertex is (1,4) and is a maximum1/2(1)2) vertex is (-1,2)adisa max2) Use partial factoring to determine the vertex of each function. State if the vertex is a max or min.a) ( x) = 3x2 - 6x + 11x.ventex=0+4x-vertex:012-3=-2x2+82.32=20 = 3x 2 - 67=10:3x(x-2)0:-22(1-4)=53x=0 x-2=6-2x-0 x-430x:0 x=4vertexis (2,5) andisa MAXx=0 x = 2 vestexis (1,8) adisa min d) f(x)=2x2++12x+174:-2a+2x+4x-vertex =Ota17=2x2+12xx17x-vetex 0+(-6)20:-x2++20=2x2+12x=1=-30=2x(x+6)0 - 1x(x-2)1x-0 x-2-02x:0 K+6=6:-1x:0 x :2=51200 x-6and is a MAXe)f(x)=4x2+64x+ 156n)(x)====-3x+8x-vestex = 0+(-16)x-vertex=28:12:320 : 42 2 6 6 x--80:1x2-3x30=4x(x+16)y-vertex : 41-8)2 +64(-8)+1560(x-6)y-verters (6)2-3/3)+8=100x = c x i k12-18-16vertex is11/20vertex is (3, 2/2) - MIN.3) An electronics store sells an average of 60 entertainment systems per month at an average of $800more than the cost price. For every $20 increase in the selling price, the store sells one fewer system.What amount over the cost price will maximize revenue?Revenue : (cost)(# sold)x-vertex 40160vertex is (10, 50000)0 : (800120x) (60-x)TT:10ofrevenueincreases800+202.0 10-x:020x==800 x=60y-vetex [800120(10)][60-10]cost = 800+20(10)x=-40(1000)(50)$1000500004) Last year, a banquet hall charged $30 per person, and 60 people attended the hockey banquet dinner.This year, the hall's manager has said that for every 10 extra people that attend the banquet, they willdecrease the price by $1.50 per person. What size group would maximize the profit for the hall this yearand what would the maximum profit be?Profit = (cast)(# of people)x-vestex : 20+(-6)veter is (7,2535)2R# of7profitdecreases30-1.5x060H0x0y.vertex [30-1.5(7)]](60+10(7)]30:1.5x xx6(19.5)(130)A group of 130 peoplecost peoplex:20would give a max prefit2535of $2535 5) The path of a rocket is given by the function, h(t) = -3t2 + 30t + 73, where 'h' is the height in metersand 't' is the time in seconds.) What is the maximum height of the rocket?h(t) -3(tP-iot)+73vertex is (5, 148)timeheight-3(t7-10t+23)+75+73-3(t-5)*+148Max height B 148m.b) At what time does the rocket reach its maximum height?5 seconds.Answers1) a) (-7,-63) min b) (3,8) min c) (27-5) min d) (-3,-2) min e) (1,4) max f) (-1,2) max2) a) (1,8) min b) (2, 5) max c) (1,5) max d) (-3,-1) min e) (-8, -100) min3) $1000JA group of 130 would give a max profit of $25355) a) 148 m b) 5 seconds