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

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

$VI$

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Oregon State University

Harvey Mudd College

Baylor University

University of Michigan - Ann Arbor

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

Oklahoma State University

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