Digital SAT Math - Ottocento #16 Advanced Quadratics (FREE WKSHT)

Lesson #16 in Kyle's Digital SAT Math Ottocento Course is about Advanced Quadratics! Learn everything you need to know about this topic from an 800 SAT Math scorer.
Download the free worksheet for this lesson here:
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You can download the Bluebook app to take Digital SAT Practice Tests here:
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You can check out Desmos Tools here:
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For more info on my tutoring services check out my website:
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Correction:
16:01 should read sum = 4 + 8 = 12 (typo)
#digitalsat #digitalsatmath #desmos

[@vortexfitness44]

Dude thank you so much for this video, this topic was the exact topic I needed to review, I couldn't find a video going as in-depth as you did here. You were extremely helpful, explanations super easy to understand. Thanks again, I subscribed! :)

[@Tutorllini]

You're welcome man! Thanks for subscribing :)

[@vortexfitness44]

@@Tutorllini I've been binging your videos lately, and I just want to say I really hope I can get my first SAT which was just last June from 1400 to 1500+... Not sure if its possible, but I'll keep you updated on my score :)

[@vortexfitness44]

I’m taking it this august btw

[@Tutorllini]

@@vortexfitness44 Awesome man! Don't forget to stop by the Community Tab once scores release: www.youtube.com/@Tutorllini/community I checked your channel - Keep up the studying and content grind!

[@akarshkollu2573]

Bro this is actually so useful. Im taking October SAT and you made the most challenging SAT questions seem so simple. THANK YOU!

[@Tutorllini]

You're welcome man! Keep me posted on your progress - stop by Community Tab after your exam to let me know how you did. Keep it up!

[@OnBabyTTV]

I know you get a lot of thanks, but my god thank you man, I'm so glad i found your channel on accident by some reddit link - because I've never studied like this before with so much engagement and I feel really good about the OCT sat (no jinx)

[@Tutorllini]

That's awesome man! I am glad to hear you understand the test better. Make sure you let me know how it goes by stopping by the Community Tab after. All the best - you got this!!!

[@amirasvlog3247]

Your teaching style is awesome. Appreciate your hard work.

[@bibeksubedi2909]

GOATED FOR 800, thanks buddy

[@Tutorllini]

You're welcome Bibek!

[@beavercollection2.029]

Thank you much

[@diixlorr]

for question 9 instead of doing all that you just get the h= -3.5 then (a) is greater than 3 so 4 then -3.5= b over 2(a) make your calculations b=28 the 3b-2a goes to 3(28) - 2(4) = 76. i wish that could help if you were running out of time

[@ajwadshine4638]

Thank you so much! Could you make a video with all the formulas review for the DSAT?

[@ohboi7701]

Hi, I have a question regarding the question at 52:04. What is the meaning of "must be true"? If we established that c

[@Tutorllini]

do you agree that any number smaller than -2 is ALSO smaller than -1? If you still don't believe me, look at this graph: www.desmos.com/calculator/sq4riyu1sd See how the red is ALWAYS inside the blue? Imagine you told me you had fewer than 5 dollars. And I said "you must have less than 12 dollars". Really weird thing to say - but true - no?

[@pongpich3354]

but if c

[@Tutorllini]

@@pongpich3354 See you have it backwards! You are taking the choice as the conclusion when you should be taking "C < -2" as the conclusion (AKA the truth). What is your goal score? Have you ever covered a logic unit (usually in a geometry or discrete math class)? When you have a logical statement of the form: p → q a counterexample (proving it false) takes the form: p → NOT q So the statement relating our conclusion and the answer choice is: If c < -2, then c must be < -1 So a valid counter example would take the form: If c < -2, then c is NOT < -1 or in other words: If c < -2, then c is ≥ -1 Take a look at this Desmos graph: www.desmos.com/calculator/qv7mjlnrd9 See how none of the green values touch the red area at all? No overlap means no counterexamples. You are trying to use the form: q → NOT p which is not how counterexamples work unfortunately. No joke - the concept of a counterexample (though poorly explained) is strongly alluded to in Bluebook app SAT Practice Test #2, Module 2B, Question 22 in College Board's answer explanation. It seems College Board expects you to have some understanding of how counterexamples work. Here is a video that covers this concept: kzbin.info/www/bejne/qoaWm4Z3gN6nitU I hope this helps!

[@KhananPaktiawal]

Hi sir, thanks this helped and was more relevant to the type of questions on the DSAT. Could you please recommend some platforms to practice these types of questions except khan academy, thanks.

[@factoverse261]

hello sir why dont you upload videos on english reading and writing topics you explain every topics with such a great details

[@factoverse261]

hey can you please upload a detailed video on algebric word problems

[@ailupipip]

Hello! I have a question in Skill 3 advanced parabolas, the first problem. To solve if is c was greater than 10 I did the following: I said, oh ok if K > 0, then it could be 1. If K is 1, then the highest value that Y could take must be one. Therefore, the y-intercept in that case couldn't be 10 because it would be too high. And, since the questions says ''must be true'', I thought my reasoning was fine. Then I saw the solution and thought it also made sense, ofc. I was just wondering if my reasoning was ok, and if this type of thinking could work in other questions, or if I was just lucky. Thank you for your videos!

[@Tutorllini]

Hi! So the logic is sound. Essentially you found what is called a COUNTEREXAMPLE: www.desmos.com/calculator/rxazihadul When you make k = 1 (valid) you get c = -14 (invalid) so it shows it is not always true that c > 10. My only caution is that searching for a counterexample in this manner would have wasted A LOT of time if that answer choice actually had been correct (because you wouldn't be able to find a counterexample since it would be true always) so ... neither good nor bad - very useful if you can quickly find a counterexample though. I hope this helps!

[@ailupipip]

Got it! Thank you!

[@Tutorllini]

@@ailupipip Please please stop by the Community Tab once you get your SAT scores and tell me how you did: www.youtube.com/@Tutorllini/community Best of luck!!!

[@oyeitsmilangaming7386]

Thanks buddy .

[@josmithajoseph1352]

For question 6, I thought because c is less than -2 1st roman numeral would be wrong. Why is that right tho?

[@Tutorllini]

Any number smaller than -2 is ALSO smaller than -1. See how the blue is encapsulated within the red? www.desmos.com/calculator/caeszulkrj

[@josmithajoseph1352]

@@Tutorllini Oh, okay ty

[@collin7687]

@@Tutorllini but what about that red area, -1.5 is not less than -2 and if you put -1.5 into the equation it results in there being two real solutions. So shouldn't c

[@Tutorllini]

@@collin7687 Does this clear things up for you? www.desmos.com/calculator/3ach3osup6 This is like if I said "I have an even amount of dollars greater than 10 dollars" and you said "you could have 7 dollars which is odd!" but $7 isn't even in the running to be considered because it isn't greater than 10 - therefore can't disprove what I said. I hope this helps!

[@hussainosman9028]

Q6 - to find c, couldn't we use the sum formula by putting c/a = -5 + 7 which would've given c=-4?

[@Tutorllini]

Not quite. The sum formula is -b/a (product is c/a). Seems like you mixed them up. Remember that the symmetry for f(u)=f(v) does NOT hold for product (it only holds for sum and midpoint/h). So the sum of the solutions IS -5 + 7 = 2 but the product IS NOT NECESSARILY (-5)(7) = -35. Does this clear things up?

[@hussainosman9028]

@@Tutorllini ohh ok yeah i mixed them up thanks

[@AmazingTVIndia143]

Pls make video on probability.....thnx

[@LesterOrie-mj6hq]

How can you solve question three algebraically? I plugged in 518 for h(t) and then subtracted over the 567 to get -49. Then I divided -49 by -16 to get 3.0625. I then took the square root of both sides to eliminate the square on the left and it became the square root of 3.0625 which equalled 1.75. Then I added four on both sides and it resulted in 5.75 seconds. I plugged it back in and I got 518 as the height. The only way I think that I went wrong is that I found the second time it reached 518 and not the first. Can you help me in this regard? Thank you for your time and assistance. Edit: I checked it on Desmos and I did in fact find the second time it reached 518. How can it be done algebraically for the first time?

[@Tutorllini]

Great question! You forgot the ± sign when taking the square root of both sides. See below: drive.google.com/file/d/1MPdu1JxEWkWP30-islvwAI_IG3ZFQB0D/view?usp=sharing Does this clear things up for you?

[@LesterOrie-mj6hq]

@@Tutorllini Thanks for the clarification. I would have utilised the Desmos calculator to ascertain for sure which came first as you did. This helps going forward.

[@mihikaasingh1623]

hello , at 22:15..how do we know the second statement MUST be true, like yes it is greater than -1 but what about the equal to sign..would appreciate a reponse cause im giving the august sat, thank you!! ur my fav channel

[@Tutorllini]

Hi! It seems you don't understand how to read inequalities. www.desmos.com/calculator/fpfqjyhd9o For a longer overview here is a video on inequalities: kzbin.info/www/bejne/o5irgGCYqKh3qKM The word OR literally means "one or the other" not both. Does this clear things up for you?

[@mrloser699]

hey man i couldnot got the desmos concept really here if i can do it with hand clearly it's worth too right😉

[@hoopz_edit]

16:06 sum of the solutions is 4+8 =12 , not 4+6, simple typo 😄

[@Tutorllini]

thanks mate I'll add a Correction when I can (edit: done!)

[@hoopz_edit]

@@Tutorllini thanks!!!

[@Mathophilia007]

Are the questions in the worksheet from the Bluebook tests ?

[@Tutorllini]

I wrote all the questions in the worksheets myself.

[@hihi-wf6vr]

Q6, Where do you get the formulas for h and b from? Can you please write them?

[@Tutorllini]

Covered here, please make sure you are watching the prior videos. kzbin.info/www/bejne/i5LTeGtorN2gq68

[@beavercollection2.029]

How many aura point do I get if I score 800 on math

[@Tutorllini]

ottocento

[@MuizatAyoola-Abioye]

i have a question. Why is 4 greater or equal to three in question 6? it literally says equal to 3, shouldn't that be not necessarily true for all cases since 4 cannot equal 3

[@Tutorllini]

Hi! The word OR in English means one or the other. So it is Greater than OR equal (not necessarily both). If that doesn't help here is a picture (see how the blue 4 is in the red solution set?): www.desmos.com/calculator/dyopj7qjvs You can also see this video: kzbin.info/www/bejne/o5irgGCYqKh3qKM I hope this helps!

[@annatee6510]

hello,i don't get the a+b+c part pls,Like how we solved to prove the others are negative and the correct answer is positive

[@Tutorllini]

Hi! I don't understand what you are asking. Try use a timestamp and be specific!

[@annatee6510]

@@Tutorllini oh I’m sorry about that.I meant at 30:35

[@Tutorllini]

@@annatee6510 You don't have to do that solving - that is just there for you to convince yourself if you still weren't sure. I'll cover choice D and you can do the rest. www.desmos.com/calculator/2u4rmmyf4c Does this clear things up for you?

[@asadali6563]

52:03 b=4 and the answer choice says b is greater than or equal to 3 , since b is =4 it is not equal to 3 so shouldn't the option b>= 3 be wrong and the only correct answer should be c

[@Tutorllini]

4 is definitely greater than OR equal to 3. See below: www.desmos.com/calculator/uar3oviooe Does this clear things up for you? This video might help too: kzbin.info/www/bejne/o5irgGCYqKh3qKM

[@MohammadHussainMohamedAliKhan]

53:00 I dont how understand why c

[@Tutorllini]

Any number smaller than -2 is ALSO smaller than -1. See how the blue is encapsulated within the red? www.desmos.com/calculator/caeszulkrj

[@MohammadHussainMohamedAliKhan]

@@Tutorllini but what about for example -1.5 it is bigger than 1 but smaller than 2

[@Tutorllini]

@@MohammadHussainMohamedAliKhan "If c < -2 , then c < -1" For a counterexample to work, the if statement must be true. Your value of -1.5 does not satisfy the if statement so it cannot be a counterexample. For example... "If I have less than 5 dollars, then I have less than 12 dollars" "But Kyle, what if you have 8 dollars!" I don't, I have less than 5 dollars... this statement is always true. For example... "If I have less than 5 dollars, then I have greater than 3 dollars" Well I could have 2 Dollars based on if statement, but 2 is NOT greater than 3, so this is a counterexample. Statement is false. I hope this helps! Once you find a number that is smaller than -2 that is not ALSO smaller than -1, let me know because I am glad to be proven wrong :)

[@Jerry-w5k]

why is a>0 at 29:14 ? There are no real solutions so isn't it supposed to be a

[@Tutorllini]

See 26:21 . You are thinking of the discriminant (b^2-4ac) which would be less than 0. To figure out if a is pos or negative you need to draw it out and see which way to make it point. Since vertex is in Quadrant 2, only pointing up will give zero x-intercepts. Does this clear things up?

[@Jerry-w5k]

@@Tutorllini Yes I understand that now, but I am still confused on how you got a>0? Is it because it opens upwards so it can't a negative value?

[@Tutorllini]

@@Jerry-w5k Yes. opens upward => a > 0 opens downward => a < 0 as covered in Ottocento #13 on Basic Quadratics. Hope this helps!

[@Andrew-xb3hy]

Isn't question 6 supposed to be B? If you replace C with -2 and type the quadratic function in Desmos then vertex is 1,0 but the question says that k < 0 which means k cannot be 0 so C should be incorrect.

[@Tutorllini]

If you watch in my work the conclusion was "c < -2". -2 is NOT less than -2 so you cannot use it as a counterexample. Let me know when you find a number smaller than -2 that is not ALSO smaller than -1!

[@Andrew-xb3hy]

@@Tutorllini Thanks for replying! The conclusion is indeed c < -2 but c < -2 is not listed as one of the possible answers to the problem. Instead, one of the possible answers shown is c < -1. Since -2 can replace c in c < -1 and if you input the function (f\left(x ight)=-2x^{2}+4x-2) in Desmos that means c < -1 cannot be one of the possible answers since k < 0 is not true because vertex is (1,0) if c is -2 which means the answer to question 6 should be B. The only way for the answer to be C is if I. c < -2 or if k is equal to or less than 0 instead of k < 0.

[@Tutorllini]

@@Andrew-xb3hy All numbers smaller than -2 are smaller than -1. Let me know when you find a counterexample! I could say that c MUST be less than 100 (because all numbers smaller than -2 are smaller than 100). It is a silly thing to say (I know!) but true nonetheless. Best of luck!

[@Andrew-xb3hy]

​@@Tutorllini I . c < -1 Replace c with -2 for -2x^{2}+4x+c since -2 is smaller than -1 and a possible value for c. -2x^{2}+4x-2 into Desmos says k = 0 which means "I. c < -1" is not true. Therefore shouldn't the question to answer 6 be B?

[@Tutorllini]

@@Andrew-xb3hy See you have it backwards! You are taking the choice as the conclusion when you should be taking "C < -2" as the conclusion (AKA the truth). What is your goal score? Have you ever covered a logic unit (usually in a geometry or discrete math class)? When you have a logical statement of the form: p → q a counterexample (proving it false) takes the form: p → NOT q So my statement that I said to you was: If c < -2, then c must be < -1 So a valid counter example would take the form: If c < -2, then c is NOT < -1 or in other words: If c < -2, then c is ≥ -1 Take a look at this Desmos graph: www.desmos.com/calculator/qv7mjlnrd9 See how none of the green values touch the red area at all? No overlap means no counterexamples. You are trying to use the form: q → NOT p which is not how counterexamples work unfortunately. No joke - the concept of a counterexample (though poorly explained) is strongly alluded to in Bluebook app SAT Practice Test #2, Module 2B, Question 22 in College Board's answer explanation. It seems College Board expects you to have some understanding of how counterexamples work. Here is a video that covers this concept: kzbin.info/www/bejne/qoaWm4Z3gN6nitU I hope this helps!

[@a.meforyou]

In Q.6 if b=4 then why is II.b≥3 correct? b isn't 3 or 5 or 6 so that option isn't correct...?

[@Tutorllini]

Sorry - that's wrong. "I have 4 dollars." Would you agree that I have 3 or more dollars?

[@amirasvlog3247]

4+6 not equal 12 Please do correction.

[@Tutorllini]

There is already a correction at the bottom of the description

[@NihadFarajov]

Thank you 👍

[@Tutorllini]

www.desmos.com/calculator/2j95qm6txo