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In Exercises $35-42,$ sketch the graph of the equation and label the vertex.$$y=x^{2}-4 x-1$$

(2,-5)

Precalculus

Chapter 10

Analytic Geometry

Section 3

Parabolas

Introduction to Conic Sections

Piedmont College

University of Michigan - Ann Arbor

Utica College

Lectures

07:16

In mathematics, a continuo…

04:09

02:45

In Exercises $35-42,$ sket…

02:04

03:09

02:55

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03:01

03:28

03:54

In Exercises 35-42, use a …

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we have 39 number problem in which our equation is given as why. Call toe Xs Choir minus four X minus one. So little street the side First Excess Choir minus four X minds one equals Y. Let us add one to both the size X squared minus four x he called Y plus one. Now we'll be completing their Squires X minus half of four that is due whole square minus to a square equal toe Y plus one, So this will be equal to X minus tool square. Let us add to a square to both the sides. Why, plus one plus four that you wipe less. Five. So the question is X minus two holes Cortical toe Y plus five, which is in the form off X Minds at holds quite a cool, too. Uh, why minus k 14 to women's skate Overtakes at Comma K will be equal to minus two comma minus aside, not minus two. It is one of us to go on. I minus five. This is the word text, and one more thing to be noted, that is positive. That is in here. This is one. So on a piece, positive so parabola will be afford opening a poor doping parabola. Okay, now we need one more. One more point to draw the parabola to confirm it to visit his passing. So when X equal to zero, why call to minus one So we can say that? Why? Into sip zero comma minus one. So let us play. Let us plug in all these values to draw the parabola. Okay, You got it, IHS Yes! Okay, so over taxes tocar minus five. This is this away. This is X or Texas took on minus five. So two, this is X equal to two. And why I called o minus five. So they see the vortex still got minus faith. After that, the parabola passes through zero comma minus one. So X equals zero y equal to minus one. Through this parable is passing my insulin paralyzed vertically a panel it upward opening. And one more thing if this is a zero comma minus one. So since excess will be executed too. So at this point, another point through which parable is passing symmetrically tow line X equal to two will be 012344 comma minus one. So, parable a must look like this tank is omens

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