#what the frick (finding the turning point)
pure loomBOT
lunar vale
do you know why completing the square works
orchid breach
well no
lunar vale
do you know why (x + a)^2 = x^2 + 2ax + a^2 is true
orchid breach
yes
lunar vale
do you know why (x + a)^2 = x^2 + 2ax + a^2 is true
the x^2 + 2x + 1 looks like the right side of this
and so (x + 1)^2 = x^2 + 2x + 1
so x^2 + 2x + 2 can be modified to look like (x + 1)^2 + 1
orchid breach
yes so the turning point is -1,1
lunar vale
now completing the square is using some patterns in when this happens to let you do this systematiclaly
first off, lets notice the following
x^2 + 2a x + a^2
you know that if you have an x^2 + # x + # that fits this pattern, it can be written as a square, right
orchid breach
yes
lunar vale
now with something like x^2 + 6x + 5,
we almost have the pattern
we know from the "2ax" that the a in this case should be 3, right
lunar vale
yep
however we dont have a 9
so we force one to appear
you can + 9 - 9
x^2 + 6x + 9 - 9 + 5
you know that adding then subtracting the same number cant go wrong
but now you can see you have the necessary 9 to make a square
right
orchid breach
right
lunar vale
therefore (x + 3)^2 - 9 + 5
or (x + 3)^2 - 4
and youve turned x^2 + 6x + 5 into (x + 3)^2 - 4
does completing the square make more sense
orchid breach
yes but I wanted to know why that method works for finding the turning point
lunar vale
do you know vertex form
orchid breach
probably not
lunar vale
do you recognize f(x + 3) as "shifting 3 to the left"?
orchid breach
no
lunar vale
then that looks like stuff you can google and figure out on your own
if youre so much in a hurry to rush finding out the why behind this
Im afraid theres no other away around it
however theres another way
but you need to trust that a formula works for that one so it wont work out as good
do you want to see it nontheless
lunar vale
its not
you just dont know either of those things
go on khan academy and go do function transformations and also vertex form of parabola
orchid breach
but a formula isn’t an explanation for me
orchid breach
if it’s just ‘oh you use this and thats why’ so WHY does THAT work
lunar vale
have you even used khan academy before?
lunar vale
I didnt know its american to use an online website like khan academy
maybe you should try using it before giving it your critique
you havent even seen how it teaches
orchid breach
no it’s that nobody talks about it
man how are you going to start an argument over this?
never critiqued it
lunar vale
but a formula isn’t an explanation for me
you started it here
you asserted that khan academy only teaches formulas
(thats not correct)
orchid breach
if that’s what you’re trying to do then i’m good i’ll ask google
i was referring to you saying there’s a formula explanation
orchid breach
but you need to trust that a formula works for that one so it wont work out as g...
Here
lunar vale
maybe ping which statement youre referring to
so that when I recommend you a website, you saying "but I dont want a formula explained to me" doesnt get misconstrued
thats a misplaced modifier
anyways,
the "function transformations" will explain what happens with the +3 and the +4
in (x + 3)^2 + 4, those serve more general purposes and dont need to be specific to parabolas
they modify the location of where x^2 is graphed
if you had 2(x + 3) + 4, the same thing applies, it modifies where 2x is
lunar vale
the "function transformations" will explain what happens with the +3 and the +4
once you get that down, the next thing is vertex form
this will confirm your suspicion that this moving-around idea is what's moving around the vertex of the parabola
its form is a(x - h)^2 + k, where (h, k) is the vertex
when you have both of these down, youll see why "completing the square" works to find the vertex of a parabola