Completing the square?

Question

f(x)= 1/500x^2 -2x +1500

ugh i get so scared and confused when working with fractions! Details would be great.

Answer 1

first take the coefficient of x^2 out of the first 2 terms as below:

f(x) = 1/500(x^2 - 1000x) + 1500

then complete the squre on the bit in the brackets.

f(x) = 1/500( (x-500)^2 - 2500)) + 1500

then multiply out the constant in the brackets

f(x) = 1/500(x-500)^2 - 5 + 1500

finally simply the constants terms

f(x) = 1/500(x-500)^2 + 1495

Don'y forget a fraction is just a number in a different form. Hope that helps

Answer 2

f(x)= 0.002x^2-2x+1500

Equation: 0.002x^2-2x+1500

0.002(x^2-2/0.002 x)+1500

0.002(x^2-2/0.002 x+(2/0.004)^2)+1500-0.002(2/0.004)^2

0.002(x-2/0.004)^2+1500-4/0.008

0.002(x-2/0.004)^2+8/0.008

0.002(x-2/0.004)^2+8/0.008

0.002(x-500)^2+1000