Write a function in vertex form
When does y equal only k? To be thorough, reformat into vertex form, and read off the vaues of "h" and "k". And you are able to pick that out just by looking at the quadratic in vertex form.
The sign on "a" tells you whether the quadratic opens up or opens down.
How to find the vertex of a parabola
As you might remember from other videos, if we have a quadratic, if we're graphing y is equal to some quadratic expression 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. Create space on the left-hand side, and, if "a" is anything other than 1, put a copy of "a" in front of this space. Don't plan on using calculator cheats. Well, if x is equal to five and this thing is zero, you're not gonna be taking anything away from the 10 and so y is going to be equal to So let's say, I'm just gonna make this up, we have y is equal to negative pi times x minus 2. To be thorough, reformat into vertex form, and read off the vaues of "h" and "k". You'll need this space and the copy of "a" to keep your equation "balanced". And so the coordinates of the vertex here are negative two comma negative And what's the y-coordinate for the vertex? This is sometimes known as vertex form and we're not gonna focus on how do you get from one of these other forms to a vertex form in this video, we'll do that in future videos, but what we're going to do is appreciate why this is called vertex form. Well, to do that, we just have to appreciate the structure that's in this expression. This whole thing right over here is going to be greater than or equal to zero. And then what's the y-coordinate of the vertex? Notice this has been factored right over here. Multiply out the "a times the squared coefficient" part on the left-hand side, and convert the right-hand side to squared form.
For instance, if the calculator screen estimates a vertex as being at 0. So it's five comma 10 and our curve is gonna look something like this.
That is, the smallest value y can be is just k; otherwise y will equal k plus something positive. You could just say, "Hey, what is the minimum y "that this curve takes on? This one in particular is going to be an upward opening parabola, and so it might look something like this.
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