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Harvey Mudd College

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J H.

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 $

05:39

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). $ g(x) = x^2 - 8 $

04:14

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

04:50

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) = 1 - x^2 $

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Okay, so this is going to be the second example out of our determinant of a matrix. Siri's. Yeah, this one says, Find the determined and we've got negative 5 to 1 100040 So we can see that we have a three by three matrix this time. So for three by three matrix, it's a little bit trickier. And so be sure to watch the Siris for the previous example before because it actually builds upon those skills of knowing how to solve for two by two matrix. So what can also be helpful is if you watch the three d vectors Siri's then watch the video on cross product because, believe it or not, this is basically the same thing as finding the cross product Onley without the I, J and K instead of and instead of it becoming a vector at the end, it actually just becomes a number. So it actually determined number. So let's go ahead and look at it. So our process is to our first row is gonna be what we're multiplying buys. It's gonna be negative. Five time something plus two time something are actually sorry. Minus two times something plus one time Something. Now, as for that's something, we determine it by circling the thing that we're doing. So negative five. And then we cross out the row and column associated. So I'm gonna cross this up. It was going across the South, So then I have the matrix 0040 So I'm gonna go ahead and put that in here 00 for Syria. So then I'm going to go on to I've done that. So then I'm going to go on to to So for two, I'm going to circle this and cross at the row and column associative. And now I have the Matrix, the two by two matrix 10 00 So then I could go and take a one. So now, Okay, so now I'm going to circle the one cross out the Roman column Associate ID, and that's gonna leave me with 1004 as my matrix. So now at this point, now that I've set it up into this nice format now I have to find determinant of each of those two by two matrices, Which is why I said you should view the previous example first. So for that, remember, we're going to do this formation minus this information, or you can think about it as a D minus B. C. When the matrix is a B, C D. Some from here, it becomes zero minus zero. That just becomes zero. So in this situation, we have negative five times zero. So then, for this, I have this times that minus that times that which is one time 00000 also to time zero. Then for this last one again, one times floor minus zero times zero is just four. So this and this cancel out because there's just zero, and that leaves me with four. The determinant of this matrix is gonna be four. So again, just to recap our steps, our first step is to set up the template. The temple is one yet actually memorized because it's gonna be I'm the first one. I'm the two by two minus the second one. Times two by two, plus the third one times a two by two. So be careful that you're making the science correct. It's minus first and then plus, then the second step would be to, um find the determinant of each of the two by two matrices. Then the third step is just to evaluate, to simplify everything you've got, multiply and add all those things out.

Introduction to Conic Sections

Discrete Maths

Introduction to Combinatorics and Probability

Introduction to Sequences and Series

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