#solving trinomials

[math-journal]

Quadratic Formula

[math-journal2]

Book Ed1 - here — Precal 2

Book Ed2

By @sock-to-the-third (18+ blog)

Parabolas

Inequality

Exponents

.

Unit 0: Pre-Algebra

.

Algebra

Unit 1: Solve for x

Unit 2: Inequality

Unit 3: Exponent

Unit 4: Graphing

Unit 5: System of Operations

~

Algebra 2

Unit 6: Functions

Unit 7: Radicals

Unit 8: Imaginary Numbers [21]

Unit 9: Trinomial

Unit 10: Logs

Unit 11: 1/x

Unit 🍎 : Growth & Decay b^x

Unit 12: (f + g)(x)

Unit 🍑: Parent Functions

~

Precalculus

Unit 13: Inequality

Unit 14: Composite f(x)

Unit 15: Inverse f(x)

Unit 16: Radicals

Unit 17: Parabola

Unit 18: Power of i

Unit 19: Power Function

Unit 20: Dividing Polynomials [50]

Unit 21: Dividing Polynomial Functions

Unit 22: Tough 1/x

Unit 23: Basic 1/x

Unit 24: b^x

Unit 25: Graphing Logs

Unit 26: Circles [70]

Unit 27: Ellipse

Unit 28: Parabola

Unit 29: Hyperbola

[fictionkinfessions]

Schools starting up in 3 days. Wally darling is invading your local classrooms ! I do not know how to solve a trinomial.

- Wally Darling ( #🍎☎️🌀 )

🐸

[reginaldcosmic]

The problem can be factored into the expression (5x - 3) (x + 1) and if the expression were set equal to zero, you would find that x = 3/5 and x = -1 are the proper solutions, which I solved without needing to learn what a box method is. To the best of my knowledge these two answers are NOT "extraneous solutions," but it's been a while since I've done this type of college algebra. I just always liked the process of factoring a trinomial into two binomials in high school. I'm that guy!

when you gotta get your mom to help with your homework

[mathematical-cheese]

What if I just dont square these trinomials

[ceceonline]

When you grow up | pogues & child!kook!reader

Summary: Pope is your math tutor but the other pogues crash your tutoring session.

------------------------------------

After you brought home a math test that you failed last year, your mother got obsessed with your grades. You were a kook, born and raised, and because of that, not only was your life supposed to be perfect, you had to be too - which included your school work. It didn’t matter that you are only 13 years old and definitely not concerned with functions or trinomials. So your mother got you a tutor: Pope Heyward, the infamous genius kid of the Outer Banks.

Normally, he comes by twice a week and you sit at the kitchen island, doing your homework with his help while your mum either works in the garden or on her computer in the living room area. But rarely, when your mother isn’t home, Pope picks you up in Heyward‘s truck and takes you to the Wreck to do your homework drinking milkshakes and snacking fries. You’re pretty sure the only reason your mum allows this on these occasions is because she doesn’t trust a “pogue“ alone in your home unsupervised, afraid that he would destroy or even steal something. And even though you find these accusations outrageous, you’re happy about the opportunities it gives you. You love being at the wreck because it always means visits from the other pogues during your study sessions. So when Pope picked you up today for your tutoring lesson at the Wreck, you were in good spirits. But after a few solved math problems, your mood isn’t as good anymore.

„I don’t get this, Pope. I’m too dumb…“, you pout for the third time since you started trying to solve this equation ten minutes ago.

„No, you’re not. You just need to follow the same rules as we did together. You can do it if you just try to concentrate.“, he answers with a sigh, pointing to the question you worked out together in the beginning of today’s tutoring session.

You shake your head, tears already stinging your eyes: „But it doesn’t make sense. What do I do with this x? That wasn’t there before!“

Lowering your head, you throw your pencil down onto the table and really start to cry, sobs racking your body.

„No, come on, y/n. Don’t cry…“

Stroking his hand down your back to calm you down, he picks up your pencil and puts it back into your pencil case that’s sitting between your half empty milkshake glass and the bowl the fries came in.

Shaking your head, more tears leave your eyes as you sob: „Maybe I’m too stupid to understand math.“

„Nah, it’s not you. It’s like math doesn’t want to be understood.“, sounds a voice from the other end of the table.

Pulling your sweater over your hands, you wipe the left over tears off your face as you lift your head.

„Hi John B.“, you greet the new arrival with a sad smile while he sits down on the opposite bench.

„Hey guys!“, smiles Pope at the rest of the pogues that followed John B to your table. JJ gently nudges your right shoulder to get you to move a bit further up the bench to make space for him to sit down next to you as Kiara takes a seat on John B’s right side.

„Cheer up, little Y/N. I can’t do math either and look at me: I’m still awesome.“, the blonde boy next to you tries to reassure you, „You don’t need perfect grades.“

To show how serious he is, he closes your text book with a resounding bang and shoves it with more force than necessary towards the other end of the table where it tumbled off and hits the ground with a second bang. Pope cringes in sympathy with the waitress that flinches at the sudden sounds but you smile satisfied, knowing you won’t be picking it up again today now that Pope’s friends are here.

The other pogues chuckle at JJ’s statement and even though you’re still annoyed at yourself, you can’t help yourself but let a few quiet giggles slip too. This earns you a big blinding smile from JJ, who looks down on you while poking your cheek, which in turn, has you sticking out your tongue at him childishly. He may look tough on the outside but you quickly learned that JJ is a softy around younger kids. It’s obvious that he has a way with words and simple gestures that just make children fall in love with him.

Pope nods his head: „I can’t believe I’m agreeing to something JJ said but yes, being perfect is overrated.“ In order to address you directly, he leans past JJ, giving said boy the opportunity to smack Pope on the back of the head: „Hey! You guys should always agree with me. Everything I say is the truth!“

The group sat around the table laughs again at the disgruntled look the hit teenager gives his friend. Kie laughs so hard that she accidentally snorts which in turn makes the rest of you laugh even louder. Out of the corner of your eye, you can see Kie’s dad behind the counter shaking his head fondly at his daughter and her friends’ shenanigans.

„Yeah, don’t listen to your mum. Being a kook isn’t what makes life fun. Trust me, I am one.“, laughs Kiara but winces when she can see her father grimace. All of Figure Eight knows how Kie and her mum fight about her life choices. Many kooks obviously agree with Kiara’s mother that she shouldn’t hang around the „dirty boys from the Cut“ but since you met the pogues yourself, you can definitely see her reasons. They are the most tight knit group of friends you’ve ever met and way more loyal to each other than any kook would be if it wasn’t for their reputation or money.

„You can be whatever you want when you grow up. Trust me.“, John B smiles at you throwing his arm around Kie’s shoulders in an attempt to distract her which earns him a small smile from her.

Pope picks his train of thought up and adds: „Once you leave this island behind, where you came from won’t matter anymore.“

And you know that they are right. You’ve heard the stories of the kids that grew up on the Cut, some coming from the most poor families Outer Banks has, that made the big money and headlines on the mainland. Just like they tell the tales of kook children that tried to sway their way into even more power and wealth, name dropping their family’s name everywhere they went but losing every last penny they brought only to realize that whatever mighty importance they had here, didn’t matter anywhere else. The only thing they all have in common - poor and rich kids, that made it or didn’t - is the fact that they never came back. Once you leave the Outer Banks behind, you never turn back because you only get one chance to get away. If you come back, the swamps and mashes will swallow you up, the poverty or kook pressure will suffocate you.

But as stupid as it sounds, you know you won’t leave. This island may have great social inequalities and some of the most problematic people out there but it’s home. It’s the way you can see the sun go up and down behind the waves of the ocean, the way the freshly mown grass always smells a little bit stronger under the warm North Carolina sun, the way you can greet every single person on this island with their first name, the way adventure lures behind every corner. You may not like the social pressure that comes with being a kook but you like the stories the pogues tell you.

„But what if I want to stay? What if I want to be a pogue, just like you guys?“, you question which makes JJ grin satisfied but John B furrows his brows: „With all our problems?“

You shake your head: „With all the fun and adventure. With the best friends anyone could ask for.“

Looking down you whisper to yourself while shrugging your shoulders softly: „Even if my mum can’t see that.“

„But little one, we already are your friends!“, Kie exclaims standing up. She walks to your side of the table and pulls Pope out of his seat to grab your hands. Pulling you up too, she smirks: „Don’t listen to your mum. She doesn’t know what you know.“

The two boys who remained sitting also get up from their seats and join Pope where he’s following you as you’re being dragged out the restaurant by a laughing Kiara.

JJ hooks his elbow around your neck, holding you upright and also slowing Kiara down by pulling you in the opposite direction.

„You’re our little pogue.“, he says, gently rubbing his fist over your head, messing up your hair.

A high pitched giggle leaves your mouth. Yeah, those are the kind of friends that make Outer Banks worth living at.

[daddyjackfrost]

things i heard in my university level advanced functions course:

“what’s algebra.”

“i dunno how to solve a trinomial, but look! i can write boobies on my calculator.”

“can you induce a coma on yourself?”

“i have eighty different things wrong in my life and math is seventy nine of them.”

“i think i should finally make that onlyfans account.”

“do male strippers make the same as female strippers?” “maybe” “they should. we got ass.”

“would i die if i jumped from the fourth floor?” “no” “give me your pencil then.”

“gays can’t do math.” “you’re not gay.”

“it’s hard to hate this class when the teacher is nice.”

“i could do the work… or i could sleep.”

“guys, let’s just all agree to not do the work.” “no.” “fuck you, jayden.”

“yk what i just realized?” “what?” “there’s only 5 white kids in this class.” “and yet we’re the ones failing.”

“watch this!” *throws calculator at the floor*

[everyothermouse]

;-; do you know how to factor I have tsi in a week help

I'm bad at explaining math things but at the very least this should help a little bit considering I did a couple of problems for you lol

OK so for trinomials which have the following three terms in them: numberx^2 (example: x^2 or 3x^2), numberx (ex: 2x or 5x), and number (ex: 7 or 2), 1. you wanna get them in that order, as in ax^2+bx+c. 2. From there, you need to find two number that multiply to ac and add to b. 3. Then you break b up into those two numbers like so:

4. From there you factor out common factors of the two numbers in each parenthesis. if you do it right what's inside each of the two parenthesis will now be the same. 5. Then you put the two outside numbers in parenthesis as well, so that they're being multiplied by the expression that was in both parenthesis in step 4. That was confusing as hell, but for example I did number 2 for u

Number 6 is also solved with this method.

If it's the 2 term polynomial ax^2+c, you need to replace a with the square root of a (which is just 1 if the term is just x^2), replace x^2 with x, and replace c with the square root of c, parenthesis that, then multiply it by itself. For example:

1) x^2+121 becomes (x+11)(x+11)

4) 9x^2-4 becomes (3x-2)(3x+2), (we're not doing imaginary numbers so if it's a negative like -4 just have one of them positive and the other negative.)

I didnt see this on your worksheet but I'll add it just in case, if it's ax^2+bx, you just factor shit straight out of it (5x^2+10x becomes 5x(x+2))

As for 2 term polynomial ax^3+c and ax^3+bx I'm not super familiar so probably go consult the internet or a teacher :P I would look it up for u but I don't have time to read all that I've got to get back to my actual math homework lolol

Good luck, feel free to send another ask if you need something elaborated on or help with a problem :)

[math-journal]

Completing the Square

Level 1: a=1, radical

Level 2: a=1

Level 2: a= +1

Extra notes

[m47h-2]

💥Blog Entry # 1: PARABOLAS

FIRST QUARTER; 1st Week

School begins but my brain and I are still in “vacation mode”. In short I feel that I am not yet ready but here we are. The 1st week was chaotic for me because of the changing and unsure schedules, and of course, the first lessons that were being taught at the beginning of school. I’m about to share to you what I have done this week on Math and what are my thoughts and reflections at the end. Enjoy! 😎✌

🔴MONDAY

We had a meeting with Sir Ric at 9:00 AM. We have already met him last Thursday so I wasn’t surprised if we start our next meeting with him discussing the first lessons for the First Quarter. Before going through the new lesson, Sir Ric made us recap about Factoring and the Perfect Square Trinomial. He also taught us about some shortcuts that is a great advantage with me because I’m not that good at factoring, sigh. He also taught us how to get the vertex of the parabola from the equations. Then, after discussing and making sure if we understand the lesson well, Sir Ric group us in pairs and answer the assigned question to us. I was not sure of the answer I have concluded and I felt it was wrong, and so it is after Sir have shown us the answers. After classes, I was frustrated with how I solved the problem so I practiced and not just the question that was assigned on me and my pair but to all the questions of the exercise. 

Here’s how I did:

Before I answered it, I went on Youtube and see if there is a video with a clearer explanation on how to solve problems like this. Here’s the link of the vid that helped me a lot -> https://www.youtube.com/watch?v=qsA3e5lGwKo . I was so happy that I’ve finally understand, yehey!

🟠TUESDAY

I woke up early at 3:00 AM to study the learning guide 1.1 in Math and also the other lessons from the other subjects as well. I read the learning guide and I have decided to answer a given question at the end to understand it more. 

Here’s how I did:

After checking that my answer was correct, I went to sleep to get some rest and to have adequate energy for tomorrow. Fast Forward to today’s Math Level 2 meeting... Sir Ric discussed the learning guides since he wasn’t able to talk about them at our last meeting. He also taught us how to solve some tricky questions on the lgs that makes them look like a piece of cake . 

🟡WEDNESDAY

When the quiz opened and the due date was on Friday, I initially scheduled to take it on Thursday since I still have some other reqs to accomplish. I thought I have fully understand the lesson but it turns out I was wrong. I still don’t get it some things of our lesson, like how to find the endpoints of the latus rectum, or the focus, or the directrix and many more😭

🟢THURSDAY

I did say that I will answer the quiz on this day, but I still don’t get it. Then I saw the interactive lesson 1.1 and remembered that I haven’t yet finish it. After I’m done with it, I totally got it! I took the practice quiz and some of the questions I was able to answer them correctly but there is some that seems a little bit confusing for me. Overall, I feel ok in taking the quiz now🧐

🔵FRIDAY

At 3:00 AM, I took the quiz and I’ve gotta say, I was able to find it ok though. Since I couldn’t take a peek of what is my score, I just hope that I pass or at least I did good in the quiz. 

Here’s my solution to a problem-solving in the quiz:

I took me a while to figure it out because it is fraction (I have a hard time when it comes to solving fraction stuff😥) but I finally got the hang of it once I have graph the problem.

🟣REFLECTION

This week was a rollercoaster for me. I’m already stressing out for the 1st week of classes because I expected to relax a little bit since its still the beginning of the school year. Though, I’m surprised that I’m doing well despite being stressed. I just need to plan of when I will do my reqs and how much time should I devote to Math. So that’s it guys! I hope you enjoyed my blog entry for this week and see you next week for the next one. BYEEEEEEE!!!!🤞🏻😚

(I’m gonna sleep like Kana here ehe😋)

[math-journal2]

<— Unit 8 — Unit 9: Trinomials —Unit 10 —>

Unit 9: Trinomials

Part 1 —>

Properties

Need 2 Know

Factorings: see [here] & [here]

Dividing Fractions: [here]

Completing the Square

Simplifying Radicals

Imaginary Numbers (a+bi)

.

Solving for x

Quadratic —> Vertex Form

Page 23

[First]

[swagmathguy]

Solving 2nd Degree Equations 

1. Flip the equation.

0 = 3-28n+9n^2

9n^2+28n-3 = 0

2. Look for a common factor.

3. Check if it’s a perfect square trinomial.

4. Check if it’s an a = 1 trinomial.

5. Trial and error:

(9n-1)(1n-3) = 0

6. Both brackets equal 0:

9n-1 = 0

n-3 = 0

7. Solve for n.

n = 1/9

n = 3

[arielaalperstein]

2nd Degree Equations Notes

-28z + 9z^2 = -3

Get rid of the -3 on the right so that all your numbers are on the same side (+3 on both sides)

3 - 28z + 9z^2 = 0

Rewrite numbers to be in order

9z^2 - 28z + 3 = 0

Look for a common factor - if there is one: divide by the common factor, ex.     2( ... )( ... ) - if there isn’t one (like in this case) leave it and continue

Look to see if its a perfect square trinomial - if it is: rewrite it with the perfect square (2y+3)^2 - if it isn’t (like in this case) leave it and continue

Now do PSF or Trial and Error (we’ll do trial and error to practice it)

If you do Trial and Error, don’t add the signs (+-) until after you’ve found the correct factors

9z^2 - 28z + 3 = 0                                                                                                (3z   1)(3z   3) = 3z 3z    DOESN’T WORK                                                          (9z - 1)(z - 3) = -27z -z    WORKS

(9z - 1)(z - 3) = 0

Then since it all equals zero, it’s safe to assume that both of your binomials are equal to zero so you rewrite them as such. Then you solve for your variable

9z - 1 = 0  --> Add 1 on both sides                                                                      9z = 1       --> Divide both sides by 9                                                                   z = 1/9      --> Leave it as a fraction (if needed)

z - 3 = 0   --> Add 3 on both sides                                                                      z = 3        --> Leave it like this                   

Then you write your answer with a comma in the middle of both

z = 1/9 , z = 3

Then you have solved the second degree equation!

[yellowmagicalgirl]

Juliet Dies in This Chapter Four: Behind the Scenes

No, this is not the real chapter four; I’m not going to break away from my “five stages of grief” format I’ve got going for me. You’ve got to wait probably a minimum of 12 hours for the chapter to post. However, tomorrow’s chapter is gonna involve a little bit of math. How I, the author, arrived at the solution will be irrelevant to the story and thus not included in the chapter. However, as someone who enjoys simple math problems like this one, I would like to share the way I found the solution. (I will be linking to this post when I post to tumblr and AO3 as an author’s note. Sorry, FFN people, I can’t do links while using that particular posting platform.)

Without further ado, let’s start.

(x^2 – 2x – 24)/(2x^4 – 5x^3 + 3x^2) ≥ 0

So this is our starting equation. A quadratic trinomial is being divided by a quartic trinomial, and this entire fraction must be greater than or equal to zero.

The trinomial in the numerator is very easily factored by the x-method. Please note that it has been years since I first learned how to factor, and I learned the method so that B is on top and A*C is on the bottom, so this may look a little wonky depending on how one was taught Algebra I.

[Image description: An “X” is drawn in red, with numbers in the four spaces created by the lines. The numbers written in the vertical compartments are red, and the numbers written in the horizontal compartments are blue. In the upper compartment is negative two, and in the lower compartment is negative twenty-four. In the left compartment is negative six, and in the right compartment is positive four.]

In the meantime, we can easily factor out an x squared from the denominator, giving us this equation:

((x - 6)(x + 4))/(x^2(2x^2 – 5x + 3)) ≥ 0

Once again, we’re going to use the x-method.

[Image description: Another “X”, with the same formatting as the previous one. In the upper compartment is negative five, and in the lower compartment is positive six. In the left compartment is negative two, and in the right compartment is negative three.]

However, we can’t just split (2x^2 – 5x + 3) into neat and simple factors of (x - 2) and (x - 3). Instead, we need to split our B term into

2x^2 – 5x + 3

2x^2 – 2x - 3x + 3

2x(x - 1) - 3(x - 1)

(2x - 3)(x - 1)

We can insert our factored expression back into the semi-factored equation that we got (2x^2 – 5x + 3) from.

((x - 6)(x + 4))/(x^2(2x - 3)(x - 1) ) ≥ 0

Do any terms cancel out? No, they don’t. Bummer. However, now that this equation has been completely factored, we know some key aspects.

x must be greater than or equal to positive six and negative four, but we can’t stop at the numerator. x must also never equal zero, positive three halves, and positive one.

Because this is an Algebra II/Pre-Calculus problem, I’m not going to solve for every single case manually. Instead, I will be using a scientific calculator. I’d use Excel, but I can’t copy and paste a graph. The results are as follows:

x < -4 ; positive

x = -4 ; zero

-4 < x < 0 ; negative

x = 0 ; undefined

0 < x < 1 ; negative

x = 1 ; undefined

1 < x < 3/2 ; positive

x = 3/2 ; undefined

x > 3/2 ; positive

Hence, x can be less than or equal to negative four, greater than positive one, and not equal to three halves. Or, to write the answer in a more elegant way,

x ≤ -4 U 1 ≤ x ≤ 3/2 U x ≥ 3/2