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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 $

04:50

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) = 1 - x^2 $

01:03

Fill in the blanks. If the graph of a quadratic function opens upward, then its leading coefficient is ________ and the vertex of the graph is a ________.

03:21

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 $

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Okay, so this is gonna be the third example out of her. Add and subtract matrices. Siri's. It's a simplify the following. So we see that we have four different matrices, and one of them has a coefficient. So I'm gonna go in and start out with the coefficient. That's this right here. And if you don't remember how to do this, be sure to look back at the video. Siri's that details how to solve matrices with coefficients. So with the coefficient, remember, we're just using the distributive property, so each, um, item in the Matrix is gonna be multiplied by the Jew. Then I've got negative three times to, which is negative six negative zero times to which is 02 times seven, which is 14. And then two times 11, which is 22. I'm going to rewrite the rest of this, but I didn't really do anything to them yet. I'm just bringing it all down. Okay, so then from here, remember, another, like another good first step to consider is just observe the matrices and see if they are the same size is because we could Onley, add or subtract matrices that are the same size is so I'm going to go through and label them. So this first one is a two by two. Second one is also a two by two. The third one has 123 rows and two columns. So it's a three by two seconds. The last one has three rows and two columns also. So it's a three by two so that it looks like these two are the same and these two are the same, which means I can Onley add and subtract within the ones that are the same. So what that means is that I'm gonna go ahead and do that to buy to multiple Kate Earth two by two matrix subtraction. So then I'm going to get negative six minus two, which is negative eight zero minus four, which is negative for 14 minus six, which is eight in 20 to minus eight, which is 14. So then I'm gonna go ahead and look at this next set of three by choose. So then I've got three minus eight. So remember, we're just being sure that we are subtracting the things that have the same position. So this three minus eight is negative. Five four minus four is zero one minus negative. Three. So be careful for the science here because one minus negative. Three. So we've got two negatives. Becomes a positive. That's positive for seven minus negative. Four again becomes a positive. So positive. 11 Tu minus negative. Five from seven six minus negative. Six becomes positive. 12. So then, um, I've simplified this and this and then the sign between it says to add them. So this is what I have currently, but notice this is still a two by two. And this is still a three by two. So because they're not the same sized matrix, we cannot simplify this any further. And so just this right here is going to be our final answer.

Introduction to Conic Sections

Discrete Maths

Introduction to Combinatorics and Probability

Introduction to Sequences and Series

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