in-28-33-without-graphing-the-parabola-describe-the-translation-reflection-and-or-scaling-that-mus-4

Question

In $28-33,$ without graphing the parabola, describe the translation, reflection, and $/$ or scaling that must be applied to $y=x^{2}$ to obtain the graph of each given function.
$$
\mathrm{f}(x)=x^{2}+x+\frac{9}{4}
$$

Foster Wisusik · Accepted Answer

Okay. This question would like us to figure out how we can transform the graph of X squared to get this one. And the best way to see that is to complete the square to change our parabola and a vertex form. So to do this, we&#x27;re gonna have to figure out our Constance D and E, where D is be over to A and E is equal to C minus B squared over four a. So for our quadratic de would be equal to one divided by two. So 1/2 and then e is C minus B squared over for a which is 9/4 minus 1/4 or to. So now we can just use this formula to find the F of X. In Vertex form is X plus 1/2 squared plus two. So now that we know are form of our function in Vertex, we can read off the shifts. So for the left right shift, we just look at the number inside the parentheses with squaring and we see you have a positive 1/2 and a positive inside the square means negative shift so to the left. So so we shift 1/2 units to the left. And then the constant outside is just like our y intercept. Actually, it&#x27;s more of just a vertical shift, so it just means shift two units. Uh, yeah. Disregard that vertical. Why intercept comment? It&#x27;s It&#x27;s just the vertical shift. It is not the white or something I should clarify. But as you can see it, all we do is read off these constants from our Vertex form. And this corresponds to the horizontal shift in this corresponds to the vertical shift.

Aditya Balasubramanian · Answer

so right here we have the function f of X because negative X squared plus X plus two negative x squared was exposed to isn&#x27;t standard for him. You need to get into a Vertex forms that we can figure out what transformations happened. So let&#x27;s start by cleaning Square. You&#x27;ll notice that we have a coefficient negative one in this X squared, which is our largest term. That&#x27;s why I mentioned in previous videos. That&#x27;s not a good sign. That&#x27;s a hints that you need to start with. Characterization. So let us do that negative X squared. And it&#x27;s ex. Those two. Um, now we need to figure out howto get a root that one squared. We can end up with this negative X as their second term. You&#x27;ll notice if you use X minus 1/2 since 1/2 times two or negative 1/2 times two is just one. You&#x27;ll get X squared when you boil the X squared minus 1/2 X minus. Another one happens. It&#x27;s minus X, and that is the last time you&#x27;ll get plus 1/4. There&#x27;s no 1/4 around, so we have to account for that. Let us do that bye doing? Um, outside. So we have this plus 1/4 of inside, and then we have a minus one for it so that we&#x27;re not affecting the function because plus 1/4 mind some for the zero. But if you&#x27;ll notice this possible for this inside and negative. So if we move something outside have been negative, it should be cancelled out. Right? So the minus 1/4 now becomes a plus 1/4 because it was moved outside of the negative and you have someone spread by negative one. And then you just say plus two, right, So it becomes negative. X minus 1/2 squared plus 9/4. That&#x27;s what Rex is. Now let&#x27;s figure out these transformations. Its men special deal. The reflection it&#x27;s been reflected over the ex access or why equals zero, because negatives on the outside it&#x27;s been translated 1/2 units, right? It&#x27;s also been translated 9/4 units up from the original function F of X equals X squared. That is it

Foster Wisusik · Answer

Okay. This question would like us to figure out how we can transform the graph of X squared to get this function. So the best way to do this is to turn our quadratic in the Vertex form by completing the square, because then we can just read off the shifts and stretches of the graph. So what will have to do is find are constants D and E for our specific problem where d is be over to a and E is equal to C minus, B squared over for a So, in our case, we have de is equal Toby over to a which is to over to So we just have one for D and then e we have c minus b squared over for a which is negative too, minus B squared, which is four divided by four a. So we get negative three for E. So this means our function can be rewritten using our formula as X plus one quantity squared minus three. So now from here, we can read off the relevant information for our transformation. So what we have here is first inside the square tells you how much your shifting to the writer left, where positive means a left shift and negative means a right shift. So since you have a positive one, or shifting one unit to the left and then for a vertical shift, that&#x27;s just the number outside with squaring, and it&#x27;s negative three. So we&#x27;re shifting down three and

Aditya Balasubramanian · Answer

Okay, so right here we have the function X squared minus 12 x plus five. And we have to determine how it&#x27;s related to X squared. Right? So it&#x27;s kind of hard to tell right now, so let&#x27;s get into it. A factor to form and hurt in order to ascertain, like, what shifts. Translations are reflections have occurred. Yeah, And get in that package for him. We have to use competing square. Hopefully, you Bender, completing the square technique or least practiced under earlier in this chapter. And you&#x27;re good to go for this. So let&#x27;s check it out. Um, we have to do is you have to find something that, when multiplied by two, becomes this second turn negative 12 x and that is negative six x. So it&#x27;s gonna strip in. We know that our route he&#x27;s gonna be x minus six minutes. Where that nothing to square. And this effort X becomes X minus six squared. You have a plus 36 from the negative six right there. So we know you have to subtract 36 right? Because for 36 minus 36 technical zero so minus 36 plus five, so f of X equals that. Sorry, if that&#x27;s a little lopsided right there, huh? Um, f mex then becomes X minus six word minus 31. And now we&#x27;ve gotten this into usable form so that we can compare it to X squared. And if you&#x27;ll notice there&#x27;s a couple of shifts that have occurred, here are translations. As you call him, uh, you&#x27;ll notice that it has been translated six to the right, and it is also six units to the rail whenever you aren&#x27;t given and used to use it all the units and also translated a total of 31 units down, and that is it.

Foster Wisusik · Answer

Okay, This question would like us to determine how to transform the graph of X squared to get after Lex. So we&#x27;re going to do this by completing the square for our quadratic because that allows us to write it in Vertex form, where we can read off the relative shifts and other transformations. So we know that D is equal to be over to a and the E is equal to C minus B squared over for a So we just need to find these values for our quadratic. So de is be over to a, which is 6/6. So that&#x27;s one then e is equal to C minus. B squared over for a, which is three minus 36/12 which is three minus three, which is zero. So f of X is just three times x plus one quantity squared. So now we can read off how our graph got shifted from our original parabola. So the first thing we notice is that X plus one is in the squaring, and that tells us about our horizontal shift. So since it&#x27;s a positive inside, it means we have a shift in the negative direction So we shift one unit left and we don&#x27;t have any. We don&#x27;t have any term right here, so there&#x27;s no vertical shift. But we do have this three outside, so we stretch by a factor of three. But I&#x27;m using stretch more as a general term. So some may say instead, it&#x27;s shrink, but really you&#x27;re just compressed.

Aditya Balasubramanian · Answer

so I hear we have a function X squared minus six x minus seven. In its standard form of pathetic expression, we want to get this into a vertex form by completing the square so that we can actually ascertain what transformations brought it from X squared, original function or a reference function. So let us do computing&#x27;s where. So if you take a look a second term, the negative six x and you to find a route that&#x27;s proper for this will get this red pen out, and that would be native three X rays, so negative three square. So keep oil inside. You&#x27;ll see you will become X squared native three x, because there&#x27;s one in three inch right there in the first part of it. Then once again, negative three x to the inner. And then you&#x27;ll notice that if you do the last two numbers, you&#x27;ll end up with plus nine and in order account for that. Let us do this lettuce. You&#x27;re at this function, and now we have this immunity introduced. X makes you squared. You have a plus nine, right, So in Morita, avoid over affecting the overall function. Let&#x27;s just subtract right plus nine minus nine. That&#x27;s just zero. So by the negative sentiments, just bring that down from before. Certify this right here, minus 16 and now this is a form that can be compared to X squared. If you&#x27;ll notice here, you&#x27;ll see that it&#x27;s been translated three units to the right and that last 16. It&#x27;s been translated 16 units down, and that&#x27;s it.

Problem

In $28-33,$ without graphing the parabola, descri…

Problem 31 Medium Difficulty

In $28-33,$ without graphing the parabola, describe the translation, reflection, and $/$ or scaling that must be applied to $y=x^{2}$ to obtain the graph of each given function.
$$
\mathrm{f}(x)=x^{2}+x+\frac{9}{4}
$$

Answer

$\left(x+\frac{1}{2}\right)^{2}+2$

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Ann Xavier Gantert

Algebra 2 and Trigonometry

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Heather Z.

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Absolute Value - Example 1

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$\left(x+\frac{1}{2}\right)^{2}+2$

Algebra 2 and Trigonometry

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Absolute Value - Example 1

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Ann Xavier GantertAlgebra 2 and Trigonometry

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Caleb E.

Michael J.

Ann Xavier Gantert

Algebra 2 and Trigonometry