Chapter 9 - Section 9.1 - Solving Systems of Linear Equations in Three Variables and Problem Solving - Exercise Set - Page 642: 64

$.28=a$, $-3.71 = b$, $12.83 = c$ 2.12 inches

$y=ax^2+bx+c$ $(4,2.47)$ $y=ax^2+bx+c$ $2.47=a*4^2+b*4+c$ $2.47=16a+4b+c$ $(7,0.58)$ $y=ax^2+bx+c$ $0.58=a*7^2+b*7+c$ $.58=49a+7b+c$ $(8,1.07)$ $y=ax^2+bx+c$ $1.07=a*8^2+b*8+c$ $1.07=64a+8b+c$ $2.47=16a+4b+c$ $.58=49a+7b+c$ $1.07=64a+8b+c$ $1.07=64a+8b+c$ $1.07-4*(2.47)=64a+8b+c-4*(16a+4b+c)$ $1.07-9.88=64a+8b+c-64a-16b-4c$ $-8.81 = -8b-3c$ $.58=49a+7b+c$ $.58-(49/16)*(2.47)=49a+7b+c-(49/16)*(16a+4b+c)$ $.58-7.564375 = 49a+7b+c-49a-49b/4 -49c/16$ $-6.984375 = 7b-49b/4 +c-49c/16$ $-6.984375 = -21b/4 -33c/16$ $-6.984375 = -21b/4 -33c/16$ $-447/64=-21b/4 -33c/16$ $-447/64*(-32/21)+(-8.81)=(-21b/4 -33c/16)*(-32/21)+(-8b-3c)$ $14304/1344-8.81=32b/4+33*2c/21+(-8b-3c)$ $14304/1344-8.81=32b/4+66c/21+-8b-3c$ $14304/1344-8.81=8b+66c/21+-8b-3c$ $14304/1344-881/100=66c/21-3c$ $14304/1344-881*1344/1344*100=22c/7-3c$ $14304/1344-1184064/134400 = 1/7*c$ $14304*100/1344*100-1184064/134400 = 1/7*c$ $1430400/134400-1184064/134400 = 1/7*c$ $(1430400-1184064)/134400 = 1/7*c$ $246336/134400 =1/7*c$ $1283/700 =1/7*c$ $1283/700*7 =1/7*c*7$ $1283/100 = c$ $12.83 = c$ $-8.81 = -8b-3c$ $-8.81 = -8b-3*(1283/100)$ $-8.81 =-8b-3849/100$ $-8.81=-8b-38.49$ $-8.81+38.49=-8b-38.49+38.49$ $29.68=-8b$ $29.68/-8 = -8b/-8$ $-3.71 = b$ $1.07=64a+8b+c$ $1.07=64a+8*-3.71+12.83$ $1.07=64a-29.68+12.83$ $1.07=64a-16.85$ $1.07+16.85=64a-16.85+16.85$ $17.92=64a$ $17.92/64=64a/64$ $.28=a$ $.28=a$, $-3.71 = b$, $12.83 = c$ $y=.28x^2-3.71x+12.83$ September is 9th month $x=9$ $y=.28x^2-3.71x+12.83$ $y=.28*9^2-3.71*9+12.83$ $y=.28*81-33.39+12.83$ $y=22.68-20.56$ $y=2.12$