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In Exercises $35-42,$ sketch the graph of the equation and label the vertex.$$x=2(y-2)^{2}$$

(0,2)

Precalculus

Chapter 10

Analytic Geometry

Section 3

Parabolas

Introduction to Conic Sections

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07:16

In mathematics, a continuo…

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In Exercises $35-42,$ sket…

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In Exercises 35-42, use a …

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this is 36. Okay, 37 number problem. The question is X equal to y minus two whole square. So let us just with the sides and divide both sides by two. We will be having why minus two holds quite equal to one by two X minus zero. So ah, this in the form off y minus K was equal to four p x minus set. So Vertex will be at Comma K. That is zero comma two. So this is the Vertex, Okay? And since he's greater than he's gotten zero so parable will be opening right work so right, parabola. And one more thing we can say that if the plug in X equal to zero if it plugging X equal to zero. So why minus true whole squad will be equal to zero. So I will be too. This means, um, intersection of the parable of it. Why I exist. That is why intercept is zero comma to now. Others draw the parabola man to get the coordinate access over here. Okay. Yep. Yes. So this is X axis. So why access what x zero comma to so they come onto. This is the Vertex and opening is right word. And one more thing you have got. Okay, it's Vertex anyhow, X equal to zero. So we need to plug in some some another value. Because this came out with a Vertex only. So let us plug in X equal to if, uh why control? We should play gin If why call toe? Why Quito one, then excellent vehicle toe to into one minus two whole square. That is X equal toe. So when x equal toe to why called one. So parabola passes through to come out one. Okay, so this is zero comma to is the vortex and parabola passes through two comma urbanize passing through Do come out one. It's executed too. Why equal to one? So if this is true Come on. This must be toe. Come. I won This foreign must be to common tree so parabolas must look like this. Thank you so much

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