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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