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

$-\left(x-\frac{1}{2}\right)^{2}+\frac{9}{4}$

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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Harvey Mudd College

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Lectures

01:32

In mathematics, the absolu…

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02:45

In $28-33,$ without graphi…

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In Exercises $29-32,$ find…

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For each of the following …

01:48

$29-52=$ Graphing Transfor…

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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't standard for him. You need to get into a Vertex forms that we can figure out what transformations happened. So let's start by cleaning Square. You'll notice that we have a coefficient negative one in this X squared, which is our largest term. That's why I mentioned in previous videos. That's not a good sign. That's a hints that you need to start with. Characterization. So let us do that negative X squared. And it'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'll notice if you use X minus 1/2 since 1/2 times two or negative 1/2 times two is just one. You'll get X squared when you boil the X squared minus 1/2 X minus. Another one happens. It's minus X, and that is the last time you'll get plus 1/4. There'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're not affecting the function because plus 1/4 mind some for the zero. But if you'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's what Rex is. Now let's figure out these transformations. Its men special deal. The reflection it's been reflected over the ex access or why equals zero, because negatives on the outside it's been translated 1/2 units, right? It's also been translated 9/4 units up from the original function F of X equals X squared. That is it

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