You missed my group of people who watch your videos. Retired senior citizens who like math and use these videos to help keep our minds sharp. Most of your videos I’ve watched I figured out. This not so much as I initially forgot the quadratic formula when you have a negative b and negative c. Then forgot to factor for 48 to reduce more. I will now go practice this type problem more. Thankyou.❤❤❤

nearing 70 and refreshing my math skills.Thanks

got it. and after 55+ years, I still remember that formula. thanks.

rewrite as y = x² - 4x - 8. Now that we have it in the form y = ax² + bx + c. -8 * 1 and -4 * 2 = -8 neither combo add to -4 so we can not factor. we can place this equation into the form of y = a(x-h)² + k where h = 1/2(-b/a) and k = -a (h²) + c. The a, b, c terms are the same as defined by the quadratic form h = 1/2(4/1) = 4/2 or just 2 k = -1(2²) - 8 = -4 - 8 or just -12 now we have the h and k values we plug them in y = (x-2)² - 12 solve with the formulas y = h + √(-k/a) and y = h - √(-k/a) [The ( ) is used to show the k and a terms are under the root symbol] y = 2 + √(12/1) and y = 2 - √(12/1) y = 2 + 2√3 and y = 2 - 2√3 Way easier than remembering that clunky formula and also you will learn this formula anyways when trying to graph a parabola. the answers for x are the coordinates where the parabola intersect with the x axis. (read as first x solution,0 and second x solution , 0. But ONLY if a real number was given as the solutions) The c term is the y intercept and read as [0,c]. and finally the vertex is our [h,k] coordinates which are actually read as [x,y] coordinates. Long story short if a teacher has you graph a quadratic equation, the above is how it is done.

Thanks for the clarification

When b is an even number, then I use de formula from Po-Shen-Loh : x=-b/2a +- sq((b/2)²-ac) instead of the quadratic formula.

Thanks!

Good, I need ur updates

Quadratic equations are quite the logic puzzles if you think about it. If you take your time an think things through slowly you will get the correct answer. This is why teachers demand that work must be shown in case you make a mistake.

2 +/- 2radical 3

Another common mistake is forgetting the negative with the a, b, c

Pop quiz answer is called the discriminant

Balance is special. A quadratic equation is special if this is set to zero

Mmmh. The tedious chore of simplifying... I stopped at the square root of 12. 🤕

Ans={+/--2)

Ans=--2.

27:25 Made exactly the same error myself (the +2, -2)

At 9:22 you say "x - 6". Should say "x - 3".

X=2+-2sqrt3

"Quad" means four. So why isn't the highest power in a quadratic equation 4? X^4 instead of X^2.

@bobwineland9936

7 ай бұрын

I couldn't resist so I Googled your question. The word quadratic comes from the Latin quadratus which means square. Therefore the X^2 makes sense.

@terry_willis

7 ай бұрын

@@bobwineland9936 The definition of a quadratic equation is one in which the highest power is 2. I get that. I do see where it says quadratus from the Latin means square - i.e. a four sided figure with equal sides. It appears that somebody just said let's call an equation raised to the second power (X^2) a quadratic equation because a four sided figure with equal sides and angles is a "square" and thus the 2nd power got this name (X 'squared' ). Or, it could have just as easily been called a bidratic equation. However, any other word starting with quad . . . is defined as something with 4 parts. So, we have million (1), billion (2), trillion (3), quadrillion (4). Quadruplets - 4 kids. Quadrangle - rectangle formed by buildings on 4 sides. Quadrilateral - 4 sided plane figure. On and on. No one ever told me to just accept what was decided 3000 years ago. It appears to be a mathematical anomaly or convention that just stuck. I guess that happens when things evolve over a long period of time. Thanks for responding.

Discriminant

Am I the only one that finds the Quadratic Formula annoying (can't stand the reduction of it all). I would rather Complete The Square, using the Equating Coefficients method or use the Po-Shen Loh method. Who's with me?

Imaginary

Just solve the formula , too much complicatins

Discriminate