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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). $ f(x) = 1 - x^2 $

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Fill in the blanks. The graph of a quadratic function is symmetric about its ________.

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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) = x^2 + 7 $

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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 $

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Okay, so this is gonna be the third example out of our matrix equations Siri's and we've got negative three Z minus the two by one matrix of six. Negative three is equal to the two by one matrix of six. Negative 12. So currently we have a coefficient multiplied by a certain matrix minus a two by one. Matrix is equal to a different to by one matrix. And because we have just addition, subtraction and also multiplication by a coefficient, we know that we could basically just use the rules of algebra to tryto isolate for Z. The first thing we're gonna want to do is add six night of three to both sides of the equation it So once we do that, we're gonna be left with negative three Z is equal to six negative. 12 plus six negative. Three it and that is going to become 12. Negative 15 because we just add the top components and then at the bottom components. So now, currently, we've got three negative three z is equal to 12. Negative 15. So from here, I'm going to divide both sides a very equation by negative three. In order to isolate for that Z, which gives me that Z is equal to 12 negative 15 divided by negative three. The reason why this works so well is because at this point, dividing by negative three is the same exact thing as multiplying by a negative one third. And that just gives us a coefficient being multiplied to a matrix. So if we do that, then we know that our Z value becomes just you have to add or multiply. So we got Z is equal to 12 times negative, one third and then negative 15 times negative. One third. Which gives me that Z is equal to negative four on the top on the positive five on the bottom for this right here is going to become our resulting matrix.

Introduction to Conic Sections

Discrete Maths

Introduction to Combinatorics and Probability

Introduction to Sequences and Series

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