we will use
c(x)=ax²+bx+c
sub the points given
when x=2, c(x)=27
27=a(2)²+b(2)+c or
27=4a+2b+c
when x=4, c(x)=105
105=a(4)²+b(4)+c
105=16a+4b+c
when x=10, c(x)=675
675=a(10)²+b(10)+c
675=100a+10b+c
so we gots
27=4a+2b+c
105=16a+4b+c
675=100a+10b+c
eliminate c's from everybody
multiply first equation by -1 and add to 2nd and 3rd equation
the resulting 2nd and 3rd equations are shown below
78=12a+2b
648=96a+8b
multiply top equation by -4 and add to bottom
-312=-48a-8b
648=96a+8b +
336=48a+0b
336=48a
divide both sides by 48
7=a
sub back
78=12a+2b
78=12(7)+2b
78=84+2b
-6=2b
-3=b
sub back
27=4a+2b+c
27=4(7)+2(-3)+c
27=28-6+c
27=22+c
5=c
c(x)=7x²-3x+5 is da equation
to produce 5 we do
c(5)=7(5)²-3(5)+5
c(5)=7(25)-15+5
c(5)=175-10
c(5)=165
costs $165 to make 5 camera cases
