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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.$$\mathrm{f}(x)=x^{2}+x+\frac{9}{4}$$

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

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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In Exercises $29-32,$ find…

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For each of the following …

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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'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's more of just a vertical shift, so it just means shift two units. Uh, yeah. Disregard that vertical. Why intercept comment? It's It'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.

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