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

The graph of $f(x)$ is 1 unit to the left and 3 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

Campbell University

Harvey Mudd College

Baylor University

University of Michigan - Ann Arbor

Lectures

01:32

In mathematics, the absolu…

01:11

02:56

In $28-33,$ without graphi…

02:28

02:55

01:54

02:52

03:28

In Exercises $29-32,$ find…

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00:44

$29-52=$ Graphing Transfor…

01:48

01:40

Use the following graph an…

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's just the number outside with squaring, and it's negative three. So we're shifting down three and

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