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In Exercises 17-34, sketch the graph of the quadratic function without using a graphing utility. Identify the vertex, axis of symmetry, and x-intercept(s). $ f(x) = x^2 + 7 $

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In Exercises 7-12, match the quadratic function with its graph. [The graphs are labeled (a), (b), (c), (d), (e), and (f).] $ f(x) = x^2 - 2 $

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In Exercises 17-34, sketch the graph of the quadratic function without using a graphing utility. Identify the vertex, axis of symmetry, and x-intercept(s). $ h(x) = 12 - x^2 $

01:29

In Exercises 7-12, match the quadratic function with its graph. [The graphs are labeled (a), (b), (c), (d), (e), and (f).] $ f(x) = (x - 2)^2 $

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Okay, So in this video, we are going to be learning how to add and subtract matrices. So with matrices, the key thing about adding and subtracting them the very most important thing that you could get if you had to obtain one thing from this video is that you could Onley add or subtract ISS. They're at the same size. So what does it mean to be the same size? Well, we know that each matrix comes with a row Times column situation and that Siri's has to be the same. If we have a two by two and two by two, we could definitely at them or subtract them. But if we had something like a three by two and four by two, that does not work. So then some people ask, Well, what if we have a two by three and a three by two? Well, that one also doesn't work, because just because we are making up The Matrix with the same set of numbers does not mean that it works because again, this is road tents column. So the number of rows and the number of columns doesn't work. So if we have a two by three that's gonna look like this A b C T f. We're asking a three by two it's gonna look like this a b c t e f So you can see that the A B A, B C D. E s are all in the different places. So, for example, see, is over here. Where I see is over here in the second one on then the he is over here, whereas is in the middle here for that other one. That's why it doesn't work, because the major see positions would not correspond. So remember, you can Onley add and subtract if they are the same size is. So now let's look at matrix that does have same size. Let's see how we are meant to at them or subtract them. So then, if we have this example to 134 minus 54 11 0, so all you have to do is it's actually very straightforward and that you just have to think about the positions. So this is the first row First column, first row first column. So we're going to subtract them, and that's gonna become the new first row First column. So to minus five is negative three on. We're gonna put that in the same exact spot. That's where we got it. So the next one will be the first row, second column, and then the first for a second column. So one minus four is negative. Three. And again, we're gonna put it exactly where we found it. Same here. Second row First column with second row First column. So three minus 11 is negative. Eight. So we know that we're gonna put it in the second row. First column again. Same here. Second row, Second column, Second row, second column four minus zero is four. We're gonna put that in the second row. Second column. Same with adding You would just do the same as that process where you're keeping every item in the same exact position.

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