in-exercises-35-42-sketch-the-graph-of-the-equation-and-label-the-vertex-yx2-4-x-1

Question

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

Suman Saurav Thakur · Accepted Answer

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&#x27;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&#x27;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

Suman Saurav Thakur · Answer

we have 35 number problems in village like will to four X minus one. Hold square plus two is given. Okay. So little subtract two from both the size it will rewire. Minus two week will, too. Foreign two X minus one. Hold square. Okay, so Lucas was the size for X minus one whole square. You called toe? I minus two. Now, we&#x27;ll be dividing both sides before, so x minus one holds critical toe one by four y minus two. Which is a Quito, which is just like X minus. Set holds critical. Do for be why minus k for pain toe y minus k. So where takes will be at gay? That is one and to And since he is gettin zero so terrible I will pay Afford opening so shape will be like this. Now focus will be, uh this is okay. One more thing we can do one more thing. We can do it. Um, we can find the point of intersection with the parable of it. They exist, if possible. Solar This plug in x equal to zero in our question. So it will become Why? For into zero minus one. Hold squared plus two, which will be for less to equal to six. So we can say when X equals zero by a call to six. So but I wanna passes through zero comma six. Okay, so this trend rather parabola. This is why exes. This is X axis where Texas One common to so one come out. So this is the Vertex one comment to and parallel will be hoping up wars and even X equal to zero equal to six. So zero comma six will be right here. So parable it will look like this is Obama six. Thank you so much.

Suman Saurav Thakur · Answer

This is 41 number problem. Ah, give any question is why call toe Xs square was two works, So let us complete the bracket. Sorry. Could be the square. My plus one explosion Hold square minus one. So they&#x27;re just add Want to both the size it max plus one was quiet. Most of the sites express when was critical to why plus one. This is just like card, Mr. Neri, Question X minus at holds critical to why minus k. So our vortex will be the it&#x27;s comma K that is minus one comma minus one. This is the Vertex, and here it is one. So he is greater than zero. So Parable will be opening a poor like this? No, we need to find one more point. So if you plug in X equals zero who I would be called a zero. So paralyzed passing through zero Cameron zero. Well, it is bright draw using their these informations. Okay, so this silly x y plane on which we have gone a drying gonna drop parabola creditors Just make it small. Okay, so there&#x27;s an ex sexists. The sound waxes politics in minus one comma minus one. So This is the vortex. And it is our sister. Was it Obama? Zero zero Bama Zeros. Another point. Must be in minus two. Common zero and terrible lays opening up war. So this will be that.

Suman Saurav Thakur · Answer

This is a problem. Number 38 Phone number 38 in. Rigid question given is X equal toe minus three. Why? Minus one Hold squared minus two. So let us unjust Ed to the board the sides. It will be minus three. Why? Mines one hold square. So I just switched the side first. Minus three. Why? Minus one holds quite equal to express. True. So let&#x27;s divide what? Size one minus one by three. So this will be who I minus one holds quite equal to minus one by three. Ex blessed to which is in the form off this gender question. Why minus k Who&#x27;s quite called 04 p x minus that So Vertex political toe. Okay, so Vertex works will be cool Toe adds common K that is minus two comma when? Okay, so this is the vertex. Now we need one more point to draw the graph. So if he just Blufgan X equal to one when we appear in X equal to one. So okay, it will not be visible. Okay, Let us concentrate on why If y will too, toe then we need to plug in regular two here in this equation Tu minus one holds critical to minus one by three X plus two. So this will become one. So by cross multiplying, this will be three equal toe minus X plus two. So x plus two is equal to minus three. So actually equal to minus five. It means the parabola is passing through minus five, comma two And one more thing. That parabola has be negative. He is less than zero. So the parabola will be left opening. It&#x27;s only doesn&#x27;t draw the graph, my Astro Common one or in the verdicts. Why X? This is minus two on my one minus two. Come on is the Vertex and the parabola passes through minus five, comma two. So this in minus five. Mama too. Okay, this is minus five comma toe. This is so but Ebola must pass through minus five comma. Zero rolls. Arable will look like this. Thank you so much.

Suman Saurav Thakur · Answer

we have 42 number problem in which x equal toe I square Maestri was given. So let&#x27;s complete the bracket. Why am I in a three by two whole square minus nine before? Let us add nine before to both the sides explains nine before equal to why am I not three by two? Full square. So let us was the side. Why minus three by two worlds Critical toe X place nine before No the this in the form off. Why? My SK was quite equal to x minus all 14 tracks Mindsets for pain to X mindsets here for political one So Vertex will be at comma K that is minus nine by four comma three by to see the Vertex Okay, No, he is greater than zero So parable I will be opening right work Now we need to find one more point. So it is evident that X equals zero I called a zero So parable is passing through a zero comma zero Let us draw the parabola. First of all, we need to get there. That&#x27;s why plane here But okay, this is our X y plane on which were big trying our parabola Oh, okay. Yes. So we have Vortex Vortex minus nine before commentary by two. So minus nine before Mr 90.25 with negative sign. So this is 2.25 minus nine before and three by two. Minus nine were four and three by to the city over text. And it did passing through. Okay, Okay. So, minds, I&#x27;m afford anti right toe. Is the Vertex okay? This is X Excellency. Why exists? And it is this parable I also passing through the local Macedo. Okay, so this was the vertex and parable. A pass into zero comma zero. And it is I drawed opening. Yes, right. Open parabola about Ebola should look like this. Think of someone.

Suman Saurav Thakur · Answer

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&#x27;s greater than he&#x27;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&#x27;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&#x27;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

Problem

In Exercises $35-42,$ sketch the graph of the equ…

Problem 39 Hard Difficulty

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

Answer

(2,-5)

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