Answer
a) $(0, 5.6)$, $(4, 14.1)$, $(8, 52)$
b) $a=.92$, $b=-1.55$, $c=5.6$
c) Please see the screenshot.
d) 29.42 billion kilowatts
Work Step by Step
a)
$2004-2000=4$
$2008-2000=8$
b)
$x=0$
$y=ax^2+bx+c$
$5.6=a*0^2+b*0+c$
$5.6=a*0+0+c$
$5.6=0+c$
$5.6=c$
$x=4$
$y=ax^2+bx+c$
$14.1=a*4^2+b*4+c$
$14.1=16a+4b+c$
$14.1=16a+4b+5.6$
$14.1-5.6=16a+4b+5.6-5.6$
$8.5=16a+4b$
$x=8$
$y=ax^2+bx+c$
$52=a*8^2+b*8+c$
$52=64a+8b+c$
$52=64a+8b+5.6$
$52-5.6=64a+8b+5.6-5.6$
$46.4=64a+8b$
$8.5=16a+4b$
$46.4=64a+8b$
$8.5=16a+4b$
$8.5-16a=16a+4b-16a$
$8.5-16a=4b$
$(8.5-16a)/4=4b/4$
$2.125-4a=b$
$46.4=64a+8b$
$46.4=64a+8(2.125-4a)$
$46.4=64a+17-32a$
$46.4=32a+17$
$46.4-17=32a+17-17$
$29.4=32a$
$29.4/32=32a/32$
$.91875=a$
$2.125-4a=b$
$2.125-4*.91875=b$
$2.125-3.675=b$
$-1.55=b$
d)
$y=.92x^2-1.55x+5.6$
$2006-2000=6$
$x=6$
$y=.92x^2-1.55x+5.6$
$y=.92*6^2-1.55*6+5.6$
$y=.92*36-9.3+5.6$
$y=.92*36-3.7$
$y=33.12-3.7$
$y=29.42$
