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(a) Draw the graph of the parabola. (b) From your graph, estimate the $x$ -intercepts. (c) Check your estimate by finding the $x$ -intercepts exactly.$$y=(x+3)^{2}$$

(b) $-3(c)-3$

Algebra

Chapter 1

Functions and their Applications

Section 4

Quadratic Functions - Parabolas

Functions

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01:43

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x^2. The output of a function f corresponding to an input x is denoted by f(x).

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(a) Draw the graph of the …

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So the easiest way to explain this problem is if you know the transformations of a graph. Um, so a per Avalon is a just a u shape. I guess I should say quadratic is the shape of a problem. Uh, and you can double check. These points are correct by plugging into a calculator or just knowing that negative to when you square negative, it becomes a positive because negative times a negative is positive and you get this kind of shape. So then when you look at the graph that you are asked to graph with, which is X plus three squared, um, that this is the transformation that shifts the graft left. Three. If you're not sure about that, I would encourage you to start plugging in values like negative three in for X. Well, negative three plus 30 And then once you square zero, you get zero. So that's why this point got shifted to the left. Three, you know at this point will get shifted to the left three. So when I plug in negative four in for X negative, four plus three is negative. One squared is positive. One. You know, something negative to get the same answer and then negative one. When I plug that in, I give one plus three is 22 squared is four. Same thing with negative five, and this goes on forever. So that's why our graph is just shifted. Left. Three. So I'm gonna circle that it's part of that's part a of your answer. Um and then Part B is asking you to guess what your X intercept is. Well, it looks like it's hitting the X axis at negative three. That's how you can determine that. Well, in part C, you can algebraic. We find the X intercept by replacing. Why with zero. Because that's how you algebraic. We find the X intercept X from y zero. So then you can square root both sides of the square 200 and subtract three over. And I'll tell you the X intercept and zero minus three is in fact, negative three. So we did that correctly. That's your final answer. A B answer

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