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Campbell University

Oregon State University

Harvey Mudd College

University of Michigan - Ann Arbor

06:27

J H.

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 $

03:07

Suzanne W.

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)^2 + 1 $ (b) $ g(x) = \left[\frac{1}{2} (x -1) \right]^2 - 3 $ (c) $ h(x) = -\frac{1}{2} (x +1)^2 - 1 $ (d) $ k(x) = [2(x + 1)]^2 +4 $

01:05

Fill in the blanks. The graph of a quadratic function is symmetric about its ________.

05:24

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 $

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Okay, So in this video, we are going to be talking about matrix equations. So matrix equations are basically just equations that involves, um, matrices that involve a little bit of algebra to solve. So the things that you could really do with matrix equations are adding matrices, subtracting matrices and also multiplying or dividing, but only by a coefficient to not by the Matrix itself, but by the coefficient. Because the multiplying by a matrix will come later. Multiplying dividing my matrices will come later on when we talk about determinants. But for now, we're going to deal with adding subtracting and multiplying or dividing by a coalition. So, like I said, the same rules of basic algebra still apply in this situation, meaning that if we had something like two X plus three is equal to seven. In order for us to isolate this X value, we would first have tracked away the three leaving us with two x is equal to four and then divide both sides by two, giving us access equal to two so same thing instead of that, If we had two x plus this, uh, two by two matrix of 2468 and that is equal to one. For negative to seven. We would have to do the same thing and subtract this matrix from both sides of the equation. When we do that at that point, we would have to x is equal. Thio, you have this. So we're just me basically doing the same thing. And at this point, we know how to deal with that because we learned how to subtract matrices. Then once you get the value of that which would become one minus two is negative one for minus 40 negative two minus six. This negative 87 minus eight is negative one that is equal to two X. And at that point we would know that we have to divide both sides of the equation by two, which essentially is the same thing as multiplying both sides by negative one half or positive one half. Sorry. At which point here let me get rid of some space and work up here. So at which point it would become the same exact thing. So X is equal to one half. It's negative. 10 negative 81 So that would become the same thing as multiplied by a coefficient, which we've also already learned how to do so that would become negative one half zero negative four and negative one half. So this would be a result in the Matrix. So again, you basically just have to use the same rules of algebra to try to isolate a variable just with matrices.

Introduction to Conic Sections

Discrete Maths

Introduction to Combinatorics and Probability

Introduction to Sequences and Series

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