Question

Write the function f(x) = ax^2 + bx + c in completed square form. SHOW YOUR WORK!!!

Answer 1

How about you showing the first two steps, and I will continue from there ?

Answer 2

i dont know how

Answer 3

Now is 0:37 AM in Bosnia.

I have to go to sleep and I'll write a solution for you.


f(x) = a x² + b x + c =

a [ x² + ( b / a ) x ] + c =

a [ x² + 2 ( b / 2a ) x ] + c + ( b / 2a )² - ( b / 2a )² =

a [ x² + 2 ( b / 2a ) x + ( b / 2a )² ] + c - ( b / 2a )² =

a ( x + b / 2a )² + c - ( b / 2a )²


f(x) = a x² + b x + c = a ( x + b / 2a )² + c - ( b / 2a )²

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Remark:

( m + n )² = m² + 2 ∙ m ∙ n + n²

In tis case:

( x + b / 2a )² = x² + 2 ∙ ( b / 2a ) ∙ x + ( b / 2a )²

So

x² + 2 ( b / 2a ) x + ( b / 2a )² = ( x + b / 2a )²
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Answer 4

Thank you so much!!! :)

Answer 5

WellHello!