Question 904410: Do I have this quadratic to standard form problem correct?
http://i.imgur.com/Gfi94o9.png?1
Thanks Answer by Theo(13342) (Show Source):
let me show you how to do it and you should be able to see where you went wrong.
start with g(x) =
factor out the 5 to get g(x) =
complete the square within the parentheses to get g(x) =
simplify by applying the distributive law of multiplication to get g(x) = which can be simplified to .
simplify further by combining like terms to get g(x) =
to determine if the standard form is equivalent to your original form, then simply pick a value of x at random and solve each of the equations for that value of x.
for example:
when x = 20, the original equation becomes g(20) = + 55 which becomes g(20) = 1455.
when x = 20, the standard form equation becomes (g(20) = which becomes g(20) = 1455.
both forms give you the same answer which is a good indication that you translates correctly.
factoring by completing the square is tricky until you get the hang of it.
you have to do a few before you become comfortable with it.
some instructions will have you separate out the constant term.
it winds up being the same thing with perhaps one less computation.
let me do it that way so you can see how it's done.
start with g(x) = as before.
separate the x terms and the constant terms so they will be shown separately as follows:
g(x) =
the 5x^2 - 30x has been enclosed in a set of parentheses to group those terms together.
now factor out the 5 from the x terms to get g(x) =
now take half of the coefficient of the x term and complete the squares to get g(x) =
why did you have to subtract the 9?
before we go through that, the 9 is the result of half the coefficient of the x term squared.
when you take x^2 - 6x and take half the coefficient of the x term and replace it with , you get .
this means you have 9 more than you wanted.
the 9 happens to be half of the coefficient of the x term squared.
so you subtract 9 and you get = which results in which is what you want.
so is equal to .
all of that stays within the parentheses.
you started with g(x) = and you ended up with g(x) = .
now you want to remove the parentheses by applying the distributive law of multiplication to get g(x) = .
now you want to simplify further by combining like terms to get g(x) = .
same answer as before except you didn't factor out the 5 from the constant term.
