In this episode of Engineer In Training Exam TV, Justin walks you through a Fundamentals of Engineering Exam Review of Parabolas.
This is Part 2 of 2
In this tutorial, we will reinforce your understanding of Parabolas, begining by defining the two general equations of a parabola and then running through a few example problems.
This Fundamentals of Engineering Exam Review of Parabolas is part of the global subject Mathematics.
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Hey what’s going on everyone, it’s Justin Dickmeyer from EngineerInTrainingExam.com.
In today’s video we are going to present a Fundamentals of Engineering Exam Review of Parabolas.
We’ll start off this tutorial discussing the theory and then get in to working a problem.
So let’s start off our Fundamentals of Engineering Exam Review of Parabolas by picking up where we left off in part 1.
An equation in our unformed friendly
form and I’ve kind of just adopted that
turn but we give it term but we’re
giving it in the second form and we want
to actually convert it into the the
nicer of the two forms the first form
that we went over well we can actually
do that and let’s go ahead and go
through an example of how you would go
about doing that
let’s say that we’re given a function f
of X is equal to Nu equal to 2x squared
minus 12x plus 3 so this is the
unfriendly form or the quadratic
equation and we want it to be in the
form of f of X is equal to a X minus H
squared plus K and we want it to be in
this form so we can quickly define the
information that we need to define about
the parabola like I said the orientation
the vertex and we also want to quickly
define where the intercepts are so all
we need to do here is essentially just
complete the square however it’s going
to be slightly different than what we
went over in the past tutorials but
essentially it’s going to be it’s the
same concept that the end result is the
same so the first thing we want to do is
make sure that the x squared term has a
coefficient of 1 and so to do that we
need to factor out 2 in this case so we
got 2 is equal to X or multiplied by x
squared minus 6x plus 3 over 2 and now
the next now this is where the process
gets kind of tricky and like I said
we’re going to do we’re going to do the
the process of completing the square
here but we’re going to do a slightly
different and instead of adding the
result to both sides we’re going to add
the result and minus the result on the
same side so let’s do this to complete
the square you take the coefficient of 6
divided by 2
and square it so in this quick case
negative six we get negative three
squared which is going to equal nine so
nine is our is our constant that we now
need to add and subtract from the same
side so let me illustrate this f of X is
equal to two x squared minus 6x plus 9
minus 9 plus three half now you say this
this is net zero nine minus nine is net
zero so it doesn’t affect our equation
or the integrity of our equation it just
allows us to factor this X term right
here so let’s go ahead and do that let’s
factor we got f of X is equal to two and
now we could factor X minus three
squared minus 15 over 2 15 over twos all
I do is convert nine into a fraction
which is going to be 18 over 2 minus 18
over two plus 3 over 2 is minus 15 over
two so next all we need to do is
multiply 2 back through and we got f of
X is equal to two X minus three squared
minus 15 and now check this out we took
our not-so-friendly form and we
converted it into our friendly form and
now we can quickly quickly determine a
lot of things let’s let’s the
orientation is going to be what if you
said a is equal to two so it’s a
positive two so it’s going to be opening
upward and now we also can really
quickly define H K which will be the
last thing we do H K in this instance is
going to be three negative 15
so just just like that we were able to
convert by completing the square and
converting the not-so-friendly form into
our friendly form of the of a parabola
and determine a couple aspects of its of
its orientation so anyways that’s it
that’s a quick recap of parabolas and
the equations that revolve around them
and some of the possible questions that
you will see on the exam so if you guys
have any more questions or want to
review any more of the videos go ahead
and check out engineering training exam
com I have all the videos there as well
as here on my YouTube channel and also
uh don’t don’t hesitate to leave me a
little feedback some some suggestions if
you guys are looking for certain
tutorials or whatnot like I’ve stated in
previous tutorials I’m just here to help
you guys out you know I just want to
give you guys some value some free value
and so you guys can go ahead and prepare
and you know do things a little bit
differently and then hitting the books
you know sometimes these videos help out
sometimes they don’t just let me know if
they are and I’ll be happy to continue
to create them so anyways that’s it for
now guys you guys take care have a good
night and we’ll be talking soon
—
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