Threethumb Threethumb 5 5 gold badges 20 20 silver badges 35 35 bronze badges. This approach is fine, though if you know the constant is zero there are easier ways. Add a comment. Active Oldest Votes. And your work is all fine. Community Bot 1. Bill Dubuque Bill Dubuque k 36 36 gold badges silver badges bronze badges.
And a nice "blurb" for one's profile! It can also be done, equivalently, by "rationalizing the numerator", see e. Arturo's answer in the same thread. Sign up or log in Sign up using Google. Sign up using Facebook.
So, to decide where to set your price, use P as a variable. You've estimated the demand for glasses of lemonade to be at 12 - P. Using however much your lemonade costs to produce, you can set this equation equal to that amount and choose a price from there.
In athletic events that involve throwing objects like the shot put, balls or javelin, quadratic equations become highly useful. For example, you throw a ball into the air and have your friend catch it, but you want to give her the precise time it will take the ball to arrive. Use the velocity equation, which calculates the height of the ball based on a parabolic or quadratic equation.
Begin by throwing the ball at 3 meters, where your hands are. Also assume that you can throw the ball upward at 14 meters per second, and that the earth's gravity is reducing the ball's speed at a rate of 5 meters per second squared.
If your friend's hands are also at 3 meters in height, how many seconds will it take the ball to reach her? Stack Overflow for Teams — Collaborate and share knowledge with a private group.
Create a free Team What is Teams? Learn more. Why not always use the quadratic equation Ask Question. Asked 5 years, 9 months ago. Active 5 years, 9 months ago. Viewed 3k times. This approach helps in understanding, among others, what it means for a polynomial to have a multiple root. Add a comment. Active Oldest Votes. Of course, this method can be refined and made more efficient, but it still needs you to factorize the given polynomial expression.
Determining the type of a singularity. Using the quadratic formula: number of solutions. Practice: Number of solutions of quadratic equations. Quadratic formula review. Next lesson. Current timeTotal duration Google Classroom Facebook Twitter. Video transcript In this video, I'm going to expose you to what is maybe one of at least the top five most useful formulas in mathematics. And if you've seen many of my videos, you know that I'm not a big fan of memorizing things.
But I will recommend you memorize it with the caveat that you also remember how to prove it, because I don't want you to just remember things and not know where they came from. But with that said, let me show you what I'm talking about: it's the quadratic formula. And as you might guess, it is to solve for the roots, or the zeroes of quadratic equations.
So let's speak in very general terms and I'll show you some examples. So let's say I have an equation of the form ax squared plus bx plus c is equal to 0. You should recognize this. This is a quadratic equation where a, b and c are-- Well, a is the coefficient on the x squared term or the second degree term, b is the coefficient on the x term and then c, is, you could imagine, the coefficient on the x to the zero term, or it's the constant term.
Now, given that you have a general quadratic equation like this, the quadratic formula tells us that the solutions to this equation are x is equal to negative b plus or minus the square root of b squared minus 4ac, all of that over 2a. And I know it seems crazy and convoluted and hard for you to memorize right now, but as you get a lot more practice you'll see that it actually is a pretty reasonable formula to stick in your brain someplace.
And you might say, gee, this is a wacky formula, where did it come from? And in the next video I'm going to show you where it came from. But I want you to get used to using it first. But it really just came from completing the square on this equation right there. If you complete the square here, you're actually going to get this solution and that is the quadratic formula, right there. So let's apply it to some problems.
Let's start off with something that we could have factored just to verify that it's giving us the same answer. So let's say we have x squared plus 4x minus 21 is equal to 0.
So in this situation-- let me do that in a different color --a is equal to 1, right? The coefficient on the x squared term is 1. And then c is equal to negative 21, the constant term. And let's just plug it in the formula, so what do we get? We get x, this tells us that x is going to be equal to negative b.
Negative b is negative I put the negative sign in front of that --negative b plus or minus the square root of b squared. So we can put a 21 out there and that negative sign will cancel out just like that with that-- Since this is the first time we're doing it, let me not skip too many steps. So negative 21, just so you can see how it fit in, and then all of that over 2a.
So what does this simplify, or hopefully it simplifies? So we get x is equal to negative 4 plus or minus the square root of-- Let's see we have a negative times a negative, that's going to give us a positive. And we had 16 plus, let's see this is 6, 4 times 1 is 4 times 21 is That's nice. That's a nice perfect square. All of that over 2, and so this is going to be equal to negative 4 plus or minus 10 over 2. We could just divide both of these terms by 2 right now. So this is equal to negative 4 divided by 2 is negative 2 plus or minus 10 divided by 2 is 5.
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