😃

Well…l’ve never heard of that one before…l’ll have to decide if it beats the x method now.

There is another method on factoring with leading coefficient. Multiply the leading coefficient of x² to the constant. Do the usual factoring, then divide each constants with the leading coefficient of x². If one constant equals the whole number, retain the quotient as a factor. If the other constant is not divisible with the leading coefficient, copy that leading coefficient to x. Ex: 2x²+11x-6 Multiply 2 to -6, x²+11x-12 Factor out: (x-1)(x+12) Divide all constant by leading coefficient 2 from the original equation: (x-1/2)(x+12/2) Simplify: (x-1/2)(x+6)... Carry over the /2 from x-1/2 and transfer the 2 to x Answer: (2x-1)(x+6)

What are asymptotes? And what do they do?

Thank you for posting my requested video…there’s more to it than l thought. Oh well l’ll just have to get my thinking cap on and get stuck in 😊 once again thanks.

I’ve just seen this very informative video on parabolas, thank you. Have you ever done a video on when the parabolas,rather than go up or down,come in from the sides? I’ve been looking for a video on sideways parabolas for ages and l just can’t find one.

When you talk about pre-algebra, algebra 1, 2 etc..where would they be in terms of A levels, O levels and the like.

Very helpful topic to cover. Thank you!

Why does 2 times the square root of 30 suddenly become 2 times the square root of 3?

Omg

Have to watch a few times to get some understanding. You brought up h and k as in the standard equation of a circle. But what do h and k actually mean? Are they just letters assigned to distances for both x and y,, or do they actually refer to a particular name?

Discriminant =0 solution= -b/2a

Thanks prof❤

Thank you…that video cleared up a few things l wasn’t sure about

Why not( -12x ) +2x? i.e-12x+2x

5:03 6/4 =3/2

Brilliant thank you

Excellent…thank you, l’ve now subscribed.

As I have said, the factor by grouping was new to me. I now understand it, but still tend to use my old method. Not sure if any is quicker or easier. I simply remove the a coefficient First use it to multiply with the c ; as you do. And use the X method (again, as you do). Then simply reintroduce the a again as the denominator tin the two factors). eg: 2x^2 + 3x +1 becomes x^2 + 3x +2 Use the X method to find (x + 2) (x + 1) then reintroduce the a term (in this case 2) as the denominator in the pair i.e.: (x + 2/2) (x + 1/2) Simplify as far as possible (x + 1) or, if no simplification is possible, use the denominator as the coefficient of x: (2x +1)

Good explanation. 👍👍👍👍

I adore you!! Thank you for your help!!

@vespa2860 I absolutely love having you as a subscriber! I just learned something new today!! You are right, I was focusing of the form and action of Scientific Notation, but I was not aware, until you wrote in, that there are further laws governing the significant figures of your answers. So, if I'm understanding your comments, the final answers I gave are not technically correct because when multiplying or dividing (or adding or substracting) with numbers is Scientific Notation form, the final answer must have the same number of significant figures as the term with the fewest significant figures in the calculation! Thank you, Vespa!! And BTW Mathing friends: always complete the calculation without rounding first to avoid errors. I love waking up to new learning!

I have decided to start community college at 57,.WOW rude awakening. Math has never been my strong subject, i just found some of you videos and the only thing I have to say is thank you for helping me understand the x method. I have been trying find the best way to understand factoring quadratics and I have found it.

Vedio is great but the audio 🔉 is very law.....thank you very much.

Lovely teacher..... Thank you v much indeed

yeah, no.

Excellent

Very clear and didactic.

I’m taking college algebra and I don’t have a strong foundation in math and your videos help in solving quadratic equations . Thank you!

✌️❣️

Could you somehow extend the video slightly before posting the other video suggestions. The actual answer is covered by them (I know you can turn on subtitles or read along with the transcript)

I appreciate and support the iniciative !

Wow! Thank you very much!

Thank you v much Mum .... you' great professor.

y = 2x² -16x + 16 ( i put the problem into the proper quadratic form of y = ax² + bx + c.) Now use vertex form of y = a(x-h)² + k h = 1/2(16/2). h = 4 [the h term, is found with the formula 1/2(-b/a)] k = -2(4²) + 16. k = -32 + 16. k = -16 [the k term is found with the formula -a(h²) + c] h = 4 and k = -16 y = 2(x-4)² - 16 [this is vertex form what we already know at this point is the vertex [h,k] and the y intercept which is just the c term in the original equation.] x = 4 + √16 / √2 and x = 4 - √16 / √2. [the formula here is x = h + √-k divided by √a and also x = h - √-k divided by √a] x = 4 + (4√2) / 2 and x = 4 - (4√2) / 2 [we cant have an irrational denominator so we multiply the denominator and the numerator by √2. √x * √x just equals x] x is the solution set [4 + 2√2 , 4 - 2√2] [ I was able to factor out a 2 from the top and bottom since it was multiplication and division] This is a lot of work shown, but if I was to do this for my own purpose or to show to a teacher who knows what I am doing then all the extra work is just explanation and it took me maybe 10 seconds to get the answer.

this is vertex form essentially. Vertex form for a quadratic formula is y = a(x-h)² +k where h = 1/2(-b/a) and k = -a(h²) + c. the a b and c terms are the same as they are in the standard quadratic form of y= ax² + bx + c. so apply all this to the equation x² - 20x + 2 =o. We rewrite this as y = x² - 20x + 2. (if we set all the x terms to o we see the y intercept is 2. This is a bonus step) now we use our formula above: h = 1/2(20/1) this of course is 20/2 which is 10 k = -1(10²) + 2. this gives me -100 + 2 which is -98. (remember if there is no coefficient before a term then assume it is 1) This gives us y = (x-10)² - 98 now solve for x with the following formulas x = h + √(-k/a) and x = h - √(-k/a) [the ( ) are used to show that the √ applies to both the -k and a term] This gives us x = 10 + √98 and x = 10 - √98 (the a term is a 1 so we can ignore it here) √98 is not a perfect square. 49 * 2 also equals 98 and 49 is a square of 7 so the square root of 98 is 7√2 This means that the solution set of x is [10+7√2, 10-7√2] this and the quadratic formula are the two ways I learned how to solve quadratic equations. You just need it in the form of ax² + bx + c = 0 then you have enough information to convert it to vertex form. A lot of work shown above, but if I wasn't explaining each and every single thing it would of taken maybe 10 seconds to do.

Mathematics 10C!

This is WAY too complicated. The X-Box method can be solve so much quicker and easier and without so much guess and check. I'd be happy to show you how if you'd like.

I used completing the square. Getting: x+1=+/-sqrt6/2 Which led to: x=--1 +/-sqrt6/2 Took me way too long to realise that -1 is -2/2😅

Thank you. I need more examples.

Mark any point on the edge of the pizza as point 1. Draw a line from that point to a second point on the edge about 90° away and mark as point 2. (Being close to 90° is not critical.) From point 2 draw a second line exactly 90° from the first line and mark its intersection with the edge of the pizza as point 3. Draw a straight third line from point 1 to point 3 and cut along that line. Assume the box has straight edges at 90° angles to get the necessary 90° angle between the first two lines..

Fantastic solution, keep up the great educational, entertaining and genuinely interesting content

this demonstrates an issue that I have had - why does it have to be 0 on right hand side. Well - Now I know - if you are dealing with square -there are not mutiple roots. so you do not have to have 0 on right. but if there are multiple roots, then it has to be zero on right - so that the equation can be set correctly ( if not zero - that raises too many possible answers ). Ok, got it.

I hate quadratic formula❤

I dig this method.

An extra comment to help boost the KZbin algorithm!

Very well explained. Thank you!

Clickbait, I wanted to see the cubic formula (or the dreaded p/q!!) :( (Still good vid tho haha)

Thanks.

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