in-12-17-use-a-graph-to-find-the-solution-set-of-each-inequality-x2-3-x4-geq-0

Question

In $12-17,$ use a graph to find the solution set of each inequality.
$$
-x^{2}-3 x+4 \geq 0
$$

Finian Lickona · Accepted Answer

Okay, So in this exercise, we are given the any equality. X squared minus two X plus three. Oh, no, I&#x27;m sorry. It should be. Plus two X minus three is less than zero. And I&#x27;ve already generated the graph of this particular polynomial right here. But just for clarity. We&#x27;re gonna go ahead and factor anyways. So this factors into X minus one X plus three. And if we were to expand this, we get X squared minus a plus three x minus X minus three Anyways. Okay. So what we are looking for is the region of X values and their corresponding. Why values that satisfy this inequality? So if I were to pick, let&#x27;s say, um the number negative three, and plug this into this equation. I get negative. Three squared, plus two times negative. Three minus three equals nine minus six. Minus three equals zero. And technically, zero is not strictly less than zero. So I can&#x27;t include the value Negative three, but I can include any value. Ah, after that. So I&#x27;m gonna put an open dot right there to indicate a open interval. Now, if I were to pick any of these remaining X values like, let&#x27;s say negative to. For example, I do negative two squared plus two times, thank you. Two minus three. He goes for minus four. Minus three equals negative three, which is less than zero. So that means that this value *** too, is going to satisfy our inequality. And I hope it&#x27;s pretty clear that all of the values from negative three up to positive one are going to satisfy the inequality given here because all their outputs, like all their functional outputs, are below the X axis axis, which means they&#x27;re less than zero. So our solution region is actually going to be this entire portion of the proble below the X axis, okay?

Finian Lickona · Answer

All right. So for this exercise, we are given the inequality X squared minus X minus two is greater than zero. And we are asked to use a graft to find the solution. Set this inequality. So I have the graft generated already right here and now what we need to do is observe the graph and determine which X values create a functional output that is greater than zero. So if we were to plug in zero into our function, we would get an output of negative too. So the zero clearly doesn&#x27;t work. Likewise with any of the values on the interior of this problem. However, all of the values outside of the parabola in either direction very clearly generate functional outputs that are greater than zero. So our solution set is going to be all the points in this region and this region. Okay?

Finian Lickona · Answer

Okay, So for this exercise, we are given the inning quality negative. X squared plus six X minus five is less than zero. And I already have the graph of this&#x27;ll generated over here already. So we need to determine which X values create functional outputs that put the parade below below zero. So if we look at, like, say the value to we see that this output generates like, uh, looks like it&#x27;s about three, that&#x27;s a positive value that&#x27;s greater than zero, not less than zero. So we need to be doing is looking at all of the X values that create outputs below zero. That&#x27;s going to be all the values from it Looks like that&#x27;s a positive one, and less than that. And then here we also have a positive five and greater than that. So our solution areas are actually gonna be everything over here. Hand everything over here. Okay?

Peter Winans · Answer

All right, we have X squared minus four ax plus three. We want to know when this function is greater than or equal to zero. So the first thing we have to do we have to treat this like we&#x27;re solving a quadratic equation. So the first thing we have to do is factor this quadratic. When we factor this, we&#x27;re going to get X minus three times, X minus one. Factors that multiply to get three, but add up to negative four. So then, to find the roots, we let each factory equals zero. So if X ministry is equal to zero, he had three to both signs. We have X equals three, and if we let X minus one equals zero, we have another route at one. Now, I know when I&#x27;m solving inequalities and they&#x27;re quadratic inequalities such as this one, that my solution said is either to the left and right of these routes, or they&#x27;re all the values between these routes. So we have to determine which we have going on here, right? I don&#x27;t know which way my solution says going, so I&#x27;m gonna pick a test value, and in this case, I&#x27;m gonna pick X equals two to see if the values between one and three are part of my solution. Said If if that doesn&#x27;t check, then I&#x27;ll know which way my solutions that&#x27;s going, We&#x27;re gonna test X equals two. In other words, I&#x27;m gonna plug to win for my access that&#x27;s going to give us two minus three times two minus one, and that she either be greater than or equal to zero. Well, that&#x27;s gonna be negative one times one which is going to be negative one and negative one is not bigger than zero, is it? So the answer is no. That is not part of my solution set. So that&#x27;s Hell&#x27;s me then. But I know which way my solution sets going. My solution sat has to be all of the values to the left of one or everything good right of three. And I&#x27;m using brackets here because it said greater than or equal to. So those roots are part of my solution set. So my solution set will be the interval from negative infinity toe, one inclusive of the one or everything from three to infinity. That&#x27;s our solution set right there

Peter Winans · Answer

all right, we have four X squared plus seven. Axe is greater than or equal to negative three. And we want, uh, find the solution Set and graph the solution said on a number line. The first thing we have to do is have this so that we&#x27;re comparing 20 So the first thing I have to do is add three double sides and that will give us four X squared plus seven X plus three is greater than or equal to zero. The next thing we have to do this factor and treat it like it&#x27;s a quadratic equation. And to factor this, we&#x27;re gonna want four x squared to be four x times acts three to be three times one. So if I do a plus three and a plus one, this will give you for X squared plus four x plus three X plus three. The forex and the three X that you get will lead up to the seven X for the middle term. So these air the correct factors that we should have If we have factored properly now we will let each factor equal zero. So for X plus three with the will equal zero and X plus one well, equal zero and we&#x27;ll solve each one. So if I subtract three from both sides here I get four X equals negative three. Divide each side by four and you get X equals negative. 3/4 in here. Subtract one from each side. You get X equals negative one. So those are our roots. Now we&#x27;re looking for a solution. Set all of the values that make this inequality true. And we wanted to be greater than or equal to zero. Well, when we have greater than or equal to zero, we know that whatever our roots are our solutions that will be to the left and right of those roots. So in other words, right now I know that my solution set has to be the interval from negative infinity to negative 3/4 Mary Right, that negative infinity of negative 3/4 inclusive of the 3/4. Or we&#x27;re gonna have negative one to infinity when we graft that on the number line it will look something like this one of zero negative three forts, negative one and we will have interval to the left and from negative three fours to the right. And I&#x27;m just realizing I wrote my solution Set wrong. I apologize. It doesn&#x27;t make sense. What I just wrote does it should be the interval from negative infinity of negative one or from negative three forts to positive infinity. We&#x27;re gonna make sure we have our interval written correctly. So this right here is what we should have for our solution set.

Problem

The perimeter of a rectangle is 24 feet. a. If $…

Problem 17 Easy Difficulty

In $12-17,$ use a graph to find the solution set of each inequality.
$$
-x^{2}-3 x+4 \geq 0
$$

Answer

The solution set is $[-4,1]$

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Ann Xavier Gantert

Algebra 2 and Trigonometry

Grace H.

Anna Marie V.

Kayleah T.

Caleb E.

Absolute Value - Example 1

Absolute Value - Example 2

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The solution set is $[-4,1]$

Algebra 2 and Trigonometry

Grace H.

Anna Marie V.

Kayleah T.

Caleb E.

Absolute Value - Example 1

Absolute Value - Example 2

Ann Xavier GantertAlgebra 2 and Trigonometry

Grace H.

Anna Marie V.

Kayleah T.

Caleb E.

Ann Xavier Gantert

Algebra 2 and Trigonometry