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03:21

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). $ f(x) = 16 - \frac{1}{4} x^2 $

06:07

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

04:55

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) = \frac{1}{2} x^2 - 4 $

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 $

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Okay, so this is gonna be the first example out of our matrix equation. Siri's and we've got X minus the three by or one by three matrix 66 negative, too. And then that is equal to the one by three matrix. Four night of 99 So remember, with matrices for adding, subtracting and multiplying with coefficients. So not multiplication in general, but multiplying with coefficients. We can basically just use the concepts of algebra. So in order to isolate our X, we could just do the opposite operation of this. So currently we're subtracting this matrix. So in order to isolate X, I could add this matrix 66 negative, too. Both sides of the equation. Now we've got that X is equal to four negative 99 plus 6, 600 to. So at this point, well, now that's easy, because we have 21 by three matrices that we're looking to add together on. We know that we just have to keep the excess consistent, the wise, consistent and disease consistent. So it's gonna be four plus six in the first position. Negative time plus six in the second position, then nine plus negative two in the third position, which will simplify to 10 negative three and seven. So this right here is your resulting matrix. And if you want to check, you could easily do that because you know that you can plug that in for X. So 10 negative 37 minus 66 Negative to technically equal for negative 99 So let's China. So 10 minus six is four negative. Three minus six is negative nine. Then seven minus negative to become 77 plus two. Since there are two negative signs which combines Teoh a positive, that's nine, so it does indeed work.

Introduction to Conic Sections

Discrete Maths

Introduction to Combinatorics and Probability

Introduction to Sequences and Series

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