Thank you! The circle thing totally blew my mind! I thought it's impossible for me to figure out anything about them before I start calculus. This's very interesting x)
In short, what you do to one side of an equation, you have to do to the other to maintain equality. For a bit of a longer explanation: he added 1 and 4 to one side, so he had to add those values to the other to keep the equation equal. Consider the following: 5x = 5. You can add anything you want to one side as long as you add it to the other side, and it will continue to be true: 5x + 3 = 5 + 3. You would only subtract if you're trying to solve for some value of x, and in this case, you're still subtracting from both sides. For instance: x + 5 = 10. You would subtract five from both sides to get x + 5 - 5 = 10 - 5 or x = 5. I think too often people get in the habit of just subtracting something from one side to solve for x (or as a math teacher I once had said "move the value to the other side", which is REALLY wrong) and forget that in actuality, you're not "moving" anything, you're literally doing the same thing to both sides.
One practical application is projectile motion. The shape of a projectile's path is a parabola, if you simplify the problem to a uniform gravitational field on a planet with negligible curvature, and no air resistance. If you are solving for the range of a projectile's motion, you would end up solving a quadratic formula. The first solution is the launch point, which is a trivial answer, and the other solution is the landing point.
Another practical application is 3D rendering through ray tracing. You model a ray of light striking a sphere, and you need to know where on the sphere it strikes, and at what angle it should rebound. You will end up solving the equation for the intersection of a secant line and a circle, which will ultimately be a quadratic equation. People who program 3-D rendering software, need a computationally efficient way to solve hundreds, if not thousands of iterations of the same quadratic equation, so having a closed-form quadratic formula makes it much more efficient to compute, even if computers can use trial and error to solve the same problem.
Eddie Woo needs to be WAY more popular. He deserves tens of millions of subscribers!
Eddie is good but I'm lowkey impressed with those kids.
Thank you! The circle thing totally blew my mind! I thought it's impossible for me to figure out anything about them before I start calculus. This's very interesting x)
Eddie Woo is a genius. Love you man 😩
Very good analysis of the equation for a circle!
Thank you this is very helpful for my daughter.
Thank you Mr Woo!
6:20 Shouldn't it be y^2 -4y + 2 instead of y^2 -4y + 4 when completing the square for? y^2 - 4y?
No. You halve the -4, then square it. Half of -4 is -2, the square of that is 4.
Try the reverse: (y - 2)^2 = y^2 - 2*y*2 + 2^2 = y^2 - 4y + 4
he hasn't yet completed the square, you're merging 2 steps in one.
You should change your last name from Woo to Wow, because wow!
Now I am interestin mathematics thankyou sir
What do you mean by completing the square?
3:41
I don't understand why the (+1) and the (+4) remained positive after you transferred them to the other side of the equal sign, please explain.
In short, what you do to one side of an equation, you have to do to the other to maintain equality.
For a bit of a longer explanation: he added 1 and 4 to one side, so he had to add those values to the other to keep the equation equal. Consider the following: 5x = 5. You can add anything you want to one side as long as you add it to the other side, and it will continue to be true: 5x + 3 = 5 + 3. You would only subtract if you're trying to solve for some value of x, and in this case, you're still subtracting from both sides. For instance: x + 5 = 10. You would subtract five from both sides to get x + 5 - 5 = 10 - 5 or x = 5.
I think too often people get in the habit of just subtracting something from one side to solve for x (or as a math teacher I once had said "move the value to the other side", which is REALLY wrong) and forget that in actuality, you're not "moving" anything, you're literally doing the same thing to both sides.
eddie Wooooo000oooOOOooo !
Can someone kindly explain to me where he got the 73 from @ 3:18 ?
4+9/16=73/16 :)
You convert the mixed number into an improper fraction. Multiply the denominator by the whole number, then add the numerator
WOO SIR I NEE YOUR CLASS PLS RELEASE A ONLIN E CRASH COURSE OR RECOMMEND ME SOME BOOKS
second!
i teach like that too but my friends are super dumb to understand anuthing... i wish i have students like yours
I am completely retarded, it's official
xD
😂😂😂
first!
none the wiser for what practical use a quadratic is.
One practical application is projectile motion. The shape of a projectile's path is a parabola, if you simplify the problem to a uniform gravitational field on a planet with negligible curvature, and no air resistance. If you are solving for the range of a projectile's motion, you would end up solving a quadratic formula. The first solution is the launch point, which is a trivial answer, and the other solution is the landing point.
Another practical application is 3D rendering through ray tracing.
You model a ray of light striking a sphere, and you need to know where on the sphere it strikes, and at what angle it should rebound. You will end up solving the equation for the intersection of a secant line and a circle, which will ultimately be a quadratic equation. People who program 3-D rendering software, need a computationally efficient way to solve hundreds, if not thousands of iterations of the same quadratic equation, so having a closed-form quadratic formula makes it much more efficient to compute, even if computers can use trial and error to solve the same problem.
tell me this is not real life crash course in romance kdrama :')