Functions help.... Write the function f(x)=ax^2+bx+c?

I have the answer in my key but it's just that i don't understand it pleeeeeeeeeeze help.....





question is





write the function f(x)=ax^2+bx+c in completed square form...








answer is f(x)=a(x+(b/2a)^2+((4ac-b^2)/4a)








it really doesn't look that bad on paper it's just that when typed out it looks bad...








i have no clue how da hell c got into ((4ac-b^2)/4a)





best if you explain da whole thing cause it's confusing me








i can only work with actual numbers not jumbled variables in fractions lol

Functions help.... Write the function f(x)=ax^2+bx+c?
ax^2+bx+c = 0





Divide through be a





x^2 + (b/a)x + (c/a) = 0 ...1





consider (x + (b/2a))^2 and expand out to get





x^2 + (b/a)x + (b/2a)^2





(x + (b/2a))^2 is quite close to where we left off the proof (only 1 term out) Lets sub this in (remember to subtract (b/2a)^2





From 1





(x + (b/2a))^2 - (b/2a)^2 + (c/a) = 0





Take the constants to the RHS





(x + (b/2a))^2 = (b^2)/(4a^2) - c/a





consider that c/a = (4ac)/4a^2 (multiplied top and bottom by 4a. Now the bottoms of both farctions are the same, they can be combined to get





(x + (b/2a))^2 = (b^2 - 4ac)/(4a^2)





Square roots of both sides gives





(x + (b/2a) = (1/2a)(+-sqrt(b^2 - 4ac))





therefore





x = 1/2a)(-b +-sqrt(b^2 - 4ac))