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Match the equation with its graph (labeled I-VIII). Give reasons for your choice.

$ y = 2x^2 + z^2 $

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$VI$

01:23

Wen Zheng

01:02

Carson Merrill

Calculus 3

Chapter 12

Vectors and the Geometry of Space

Section 6

Cylinders and Quadric Surfaces

Vectors

Campbell University

Baylor University

University of Nottingham

Boston College

Lectures

02:56

In mathematics, a vector (from the Latin word "vehere" meaning "to carry") is a geometric entity that has magnitude (or length) and direction. Vectors can be added to other vectors according to vector algebra. Vectors play an important role in physics, engineering, and mathematics.

11:08

In mathematics, a vector (from the Latin word "vehere" which means "to carry") is a geometric object that has a magnitude (or length) and direction. A vector can be thought of as an arrow in Euclidean space, drawn from the origin of the space to a point, and denoted by a letter. The magnitude of the vector is the distance from the origin to the point, and the direction is the angle between the direction of the vector and the axis, measured counterclockwise.

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Match the equation with it…

00:56

00:43

00:48

01:32

02:44

02:40

01:13

okay to think about what this looks like. All you gotta do is let some variable B. Zero. So I'm going to first let X be zero. So I'm in the Y. Z. Plane. Can the Y. Z plane is the plane that the screen of your computer is in? So that's why equals E. Squared. That's a parabola. Opens up on the Y axis um and it uses it on the opens up on the positive Y axis because these squared is always positive. So it looks like this And then if I let ZB0. Now, now I'm in the uh sorry, I was in the Y. Z. Plane, I guess you can't tell what I meant there which way I was drawing it. Okay. Hillary. Try again because it should look symmetric about the Y axis there. Okay, now I'm when Z is zero, That was this one the Green one. Okay, now I'm in blue now I'm letting that was where X was zero. Now I'm letting Zb zero and I'm drawing Y equals two X squared. So I'm in the UAE explain which is like the floor here. Okay. I also have a proble, it's a little bit skinnier than the one I drew before. All right, so I have a parable Lloyd opening on the positive Y axis and it's taller in the X. Uh in the Z direction than it is in the X direction. Okay, hope that matches with one of them

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