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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.$$\mathrm{f}(x)=x^{2}-12 x+5$$

The graph of $f(x)$ is 6 units to the right and 31 units downwards comparing to the graph of $y=x^{2}$ .

Algebra

Chapter 5

QUADRATIC FUNCTIONS AND COMPLEX NUMBERS

Section 1

Real Roots of a Quadratic Equation

Equations and Inequalities

Quadratic Functions

Complex Numbers

Polynomials

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01:32

In mathematics, the absolu…

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In $28-33,$ without graphi…

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02:55

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$29-52=$ Graphing Transfor…

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In Exercises $29-32,$ find…

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Okay, so right here we have the function X squared minus 12 x plus five. And we have to determine how it's related to X squared. Right? So it's kind of hard to tell right now, so let'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're good to go for this. So let'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's gonna strip in. We know that our route he'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's a little lopsided right there, huh? Um, f mex then becomes X minus six word minus 31. And now we've gotten this into usable form so that we can compare it to X squared. And if you'll notice there's a couple of shifts that have occurred, here are translations. As you call him, uh, you'll notice that it has been translated six to the right, and it is also six units to the rail whenever you aren't given and used to use it all the units and also translated a total of 31 units down, and that is it.

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