![vertex of quadratic function vertex of quadratic function](https://image3.slideserve.com/5686140/complete-the-square-to-find-the-vertex-form-then-find-the-vertex-los-and-max-min3-l.jpg)
And then what is that lowest net value? Well it's negative 50.
![vertex of quadratic function vertex of quadratic function](https://www.wikihow.com/images/a/a1/Find-the-Vertex-of-a-Quadratic-Equation-Step-9-Version-2.jpg)
Happens at t equals five, which is at time five months. In a form, in vertex form, so it's easy to pick out this value, and we see that this low point So we hit our low point, we rewrote our function So v of five is equal to negative 50, that is when we hit our low point, in terms of the net Notice this whole thingīecomes zero right over here. So if we say v of five is going to be equal to two times five minus five, trying to keep up with the colors, minus five squared minus 50. Let me do that in a different color, don't wanna reuse the colors too much. And so this part right over here is going to be equal to zero So if you have something squared, it's going to hit its lowest point when this something is zero, otherwise it's going Minimized, think about it, you have two times something squared. Now why is this form useful? This is vertex form, it's veryĮasy to pick out the vertex. Is t minus five squared, and then we have the minus 50. To two times this business, which we already established And when you view it that way, now v of t is going to be equal So then I subtract 50 here to get to what I originally had. Is multiplied by two, so I really did add 50 here, Here, it's in a parenthesis, and then the whole expression You're saying wait, you added 25, not 50. Strange thing I'm doing, all I did was add 50 and subtract 50. So just to be clear, this isn't some kind of To continue to be true, we have to subtract 50. So in order to make the equality, or in order to allow it
VERTEX OF QUADRATIC FUNCTION PLUS
You redistribute the two, you'd get two t squared minus 20t plus 50, plus two times 25. Nilly add 25 to one side of an equation like this, that will make thisĮquality no longer true. But as I alluded to a few secondsĪgo, or a few minutes ago, you can't just willy To t minus five squared, just this part right over here. If we add 25 like that, is going to be equivalent It would be equivalent to this entire thing, So if we add 25 right over here, then this is going to becomeĪ perfect square expression. So half of negative 10 is negative five, and if we were to square it, that's 25. But the way that we complete the square is we look at this first degreeĬoefficient right over here, it's negative 10, and we say all right, well let's take half Up completing the square on Khan Academy and review that. Looks unfamiliar to you, I encourage you to look Perfect square expression? If any of this business about completing the square The value of that side, but writing it in a way so we have a perfect square expression, and then we're probably going to add or subtract some value out here. Which gets us to vertex form, is all about adding and subtracting the same value on one side. And I'm going to leave some space, because completing the square, So the first thing I will do is, actually let me factor out a two here, because two is a commonįactor of both of these terms. And the way we can do that is actually by completing the square. All right, so you can imagine the form that I'm talking about is vertex form, where you can clearly spot the vertex.
![vertex of quadratic function vertex of quadratic function](https://i.ytimg.com/vi/U9PuARECIx8/hqdefault.jpg)
Vertex of this parabola? Pause this video and think about that. So it becomes very easy to pick out this low point, which is essentially the
![vertex of quadratic function vertex of quadratic function](https://showme0-9071.kxcdn.com/files/168977/pictures/thumbs/1467934/last_thumb1395447378.jpg)
Is, is there some form, is there some way that I can re-write this function algebraically Its lowest in that value, and that's going to happen at some time t, if you can imagine that this Vertex of this parabola, where it's going to hit Some point, right over here, which really is the I don't know exactly what it looks like, we can think about that in a second. If I were to graph it, IĬan see that the coefficient on the quadratic term is positive, so it's going to be some form The function which describes how the value of the restaurant, the net value of the restaurant, changes over time is right over here. Lowest net value will be, underline that, and when Taylor wants to know what the restaurant's In thousands of dollars, t months after its opening is modeled by v of t is equal to