f(x)=1/2x^2+10x-3

Question

Write in f(x)=1/2(x+10)^2- x form 

 

Complete the Square

Answer 1

(1/2)x^2 + 10x - 3

factor out the 1/2 from the x terms

(1/2)[x^2 + 20x ] -3

complete the square in brackets, by taking half 20 and squaring it. add 100 in the brackets, which is the same as adding (1/2)(100) = 50, so subtract 50

(1/2)[x^2 + 20x +100] -3 -50

= (1/2)[x+10]^2 -53