ðŸ’¬ ðŸ‘‹ Weâ€™re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!

Like

Report

No Related Subtopics

Johns Hopkins University

Oregon State University

University of Michigan - Ann Arbor

Idaho State University

01:25

J H.

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 + 1)^2 - 2 $

06:27

In Exercises 13-16, graph each function. Compare the graph of each function with the graph of $ y = x^2 $. (a) $ f(x) = \frac{1}{2} x^2 $ (b) $ g(x) = -\frac{1}{8} x^2 $ (c) $ h(x) = \frac{3}{2} x^2 $ (d) $ k(x) = -3x^2 $

01:30

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 - 4)^2 $

02:02

In Exercises 7-12, match the quadratic function with its graph. [The graphs are labeled (a), (b), (c), (d), (e), and (f).] $ f(x) = 4 - (x - 2)^2 $

Create your own quiz or take a quiz that has been automatically generated based on what you have been learning. Expose yourself to new questions and test your abilities with different levels of difficulty.

Create your own quiz

So this is gonna be our fourth example out of our matrix Multiplication. Siris on. We've got six you to you. You squared, You ve v squared. Negative to be squared for our first matrix on the for our second matrix. We've got negative three. You won six you three v negative. Six u v. So the first thing I'm gonna do is consider what the dimensions of my matrices are. And remember, we always have to do Row column, or you can think of it as horizontal times vertical and the order does matter. So for that first matrix, we've got to rose and three columns. So it's a two by three. And for our second one, we've got, ah, three rows and two columns, so it's a three by two. So this multiplication does indeed work because the insides are the same and they need to be the same for it to work. That's kind of like a requirement in order to multiply matrices. So then, for the outside, we have a two by two, and this is what the resulting matrix is going to become. We already know what's, um Matrix. So we already know what's our resulting is gonna look like So then I'm going to write out a two by two here. Mhm. So then, for our first term, we know it's going to be this situation right here. So it's gonna be six you times negative for you. So, actually, let's go down here. So I think it's gonna take a bit of space. So six you times Negative three. You plus two you times six. You remember Because we've used these now, were you gotta use thes. And then now we've got to use the U squared and the negative six. You Okay, so then that is going to simplify. Thio? Uh, negative. 18. You squared plus 12. You squared plus U squared. Uh, let's see. This is times because you cute time six. So negative six. You cute. So that's going to simplify too. Negative. Six. You cubed minus six. You squared. Thanks that Excuse me. So that's what we have so far for the first term. So I'm just going to get rid of this and pop that right in there just to save me some space. So negative sticks to you. Cute. When a six, you squared. Okay, so now Let's go on to the second term. So for the second term, we know that we have to dio there's some of this. Okay? Eso don't you squared. Okay, So for our second term, we know that we've got to do, um, this thing times this thing because we've used that entire thing already. So if we do that, we're gonna be left with, Um See, we've got six you times one, which is six. You plus three v times to you plus u squared times be that would simplify to six you the six UV plus u squared feet. So I'm just going to replace it with that and pop that right up there. So I've got six you for six u b u v squared you square to be No, we've got that one. And now we're gonna move on to the next term, which is the one on the bottom of the first column. So for that one, we used this first row entirely, so we're not using that ever again. Now we're doing this right here, So the first one is gonna be UV times negative three you because V squared times six you plus negative to V squared times negative six You And then if we simplify that down, that would give me negative three. You squared fee plus six v squared. You plus 12 v squared You which the these two terms right here would combine into 18 b squared you. So I'm just gonna pop that right into that position, and it's gonna become negative. Three. You squared fee plus 18 V square to you. Okay, so not for our last term. So now we've used we've essentially used this one twice, so we're never using this one or this one ever again. Which means now we're moving on to this right here. When we do that, we've got one times UV, which is UV plus V squared times three V plus negative to be square times V, which simplifies to UV plus three v cute plus or minus two via cute. So then once we do that, um, these two will combine because we have a life term there that will just become vey cute. So now if I pop that into position, I will have you v plus be cute. Okay, so then my resulting matrix is going to become this one right here.

Introduction to Conic Sections

Discrete Maths

Introduction to Combinatorics and Probability

Introduction to Sequences and Series

05:39

01:51

04:28

05:15

05:16

01:39

01:42

01:36

02:08

02:41