of carpet.)Īrea of a rectangle and Landscaping/border/frame problems. Set each factor equal to 0. And solve the linear equation. Substitute the given information into the equation.Ħ. Determine if there is a special formula needed. So now, you hopefully appreciate why this is called vertex form.Steps for solving Quadratic application problems:ġ. Going to be equal to zero and y is going to be 7.1. And then if this is equal to zero, then this whole thing is Going to be the x value that makes this equal What is the vertex of the parabola here? Well, the x-coordinate is
#QUADRATIC EQUATION DEFINITION PLUS#
So let's say, I'm just gonna make this up, we have y is equal to negative pi times x minus 2.8 squared plus 7.1. Let's do one more example just so that we get really fluent at identifying the It intersects the x-axis but it's going to be aĭownward opening parabola. So it's five comma 10 and our curve is gonna Scales for the x and y-axis, but there you have it. This would be positive 27, 10 would be something like this. And so the vertex here is x equals five, and I'm just gonna eyeball it, maybe it's right over here, x equals five. And what's the y-coordinateįor the vertex? Well, if x is equal to fiveĪnd this thing is zero, you're not gonna be takingĪnything away from the 10 and so y is going to be equal to 10. Well, that of course is going to happen when x is equal to five, and that indeed is the So, where do we hit a maximum point? Well, we hit a maximum point when x minus five is equal to zero, when we're not takingĪnything away from the 10. So this whole thing right over here is going to be less than orĮqual to zero for all x's, so it could only take away from the 10. So here, this part is stillĪlways going to be non-negative but it's being multipliedīy a negative two, so it's actually always Well here, this is gonnaīe downward opening and let's appreciate why that is. X minus five squared, and then let's say plus 10. Just say negative two times x plus five, actually, let me make it x minus five. So let's say let's pick a scenario where we have a downward opening parabola, where y is equal to, let's Good at picking out the vertex when a quadratic is Now let's get a few moreĮxamples under our belt so that we can really get And you are able to pick that out just by looking at the And so the coordinates of the vertex here are negative two comma negative 27. Y is equal to negative 27, so this right over here is negative 27. What is the minimum y "that this curve takes on?" Well, when x is equal to negative two, this whole thing is zero and Y-coordinate of the vertex? You could just say, "Hey, Negative two, so we know that this x-coordinate right
Subtract two from both sides and you get x is equal to X-coordinate of the vertex, well, for what x valueĭoes x plus two equal zero? And of course we can So you could just say, if you wanna find the And so, when will this equal zero? Well, it's going to be equal to zero when x plus two is going This curve right over here, for your parabola, is going to happen when this expression is equal to zero, when you're not addingĪnything to negative 27. So another way to think about it, it's only going to beĪdditive to negative 27. This whole thing right over here is going to be greater And so this is never going to be negative and we're multiplying it byĪ positive right over here. Here, if you square it, you're never going to The important thing to realize is that this part of the expression is never going to be negative. To appreciate the structure that's in this expression. How do we do that? Well, to do that, we just have To pick out the coordinates of this vertex from this form. Is called vertex form is it's fairly straightforward The vertex right over there and you have your y-coordinate of the vertex right over here. Parabola like this, the vertex is this point right over here. It might look something like this right over here. This one in particular is going to be an upward opening parabola, and so it might look something like this. If we're graphing y is equal to some quadraticĮxpression in terms of x, the graph of that will be a parabola, and it might be an upward opening parabola or a downward opening parabola. As you might remember from other videos, if we have a quadratic, One of these other forms to a vertex form in this video, we'll do that in future videos,īut what we're going to do is appreciate why this This is sometimes known as vertex form and we're not gonna focus on how do you get from And this last form is what we're going toįocus on in this video. Notice this has beenįactored right over here. This is the equation and sometimes called standardįorm for a quadratic.
They've just beenĪlgebraically manipulated. It might not be obvious when you look at these three equations but they're the exact same equation.
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