in-exercises-57-and-58-determine-the-x-intercepts-of-the-graph-visually-then-find-the-x-intercepts-a

Question

In Exercises 57 and 58, determine the x-intercept(s) of the graph visually. Then find the x-intercept(s) algebraically to confirm your results.

$ y = 2x^2 + 5x - 3 $

J Hardin · Accepted Answer

Let&#x27;s determine the X intercept visually from the grass and then we&#x27;LL go ahead and find the ex intercepts algebraic Lee to confirm our our guest from the graph. Now let&#x27;s go on to the graph. Here we have our parabola. We could zoom in tow, find the exact values here. But let&#x27;s not do that right now because we will find them. Lt break anyways. But based on the graph, it looks like if this is too, that this is is one, then this looks to be about a half, whereas the other one looks like about negative three. So for right now we&#x27;re guessing. So that&#x27;s based on the visual guests. And now let&#x27;s go Algebraic leads to confirm. So in this case, the X and reserves are the while the values that give you equal zero. So we want to go ahead and set. This is quadratic equals to zero and then solve for X. While there are many ways to do this, one way to do this is to complete the square. Another methods to use the quadratic formula here. So if you have, then we know that we can go ahead and say the following by the contract IQ formula. Now, in our case, we have a sze to B is five c is minus three. So plugging these in into the contract IQ formula so have five squared minus four times two times of minus three and this is all over two times a day. So notice inside the radical. Here you have twenty five much out here for the double minus that turns into a plus. And then we&#x27;LL have eight times three, which is twenty four and giving this asshole of forty nine and we know the square root of that is seven. So all over four and then now I have to be simplified. So if you do the plus sign you get negative five plus seven, which is two. Divide that by four. That gives you a half. And if you do the minus sign, you have negative twelve over four, which is minus three. And these values do agree with our guests from the graph. So finally, we should go ahead and just write out these answers. Technically, the X intercept is on a number. It&#x27;s a point. So we should right one half comma zero and then negative three comma zero. And these are answers

J Hardin · Answer

Let&#x27;s go ahead and graft this proble. And based on the graph, we&#x27;LL make a guest for the eggs intercepts and then we&#x27;ll algebraic lee find X intercepts and computer results So photograph this one complied points Another method is just go ahead and complete the square So I see a four here on the X and negative for you Take half of that which is negative to square that you get four. So what I&#x27;LL do here is our ad in a four and then I&#x27;ll make up for the adding the four by subtracting for a swell. So, as you can see, we really haven&#x27;t changed the expression because these two will just cancel out Now The reason for doing this is that we could go on and simplify inside the prentiss he&#x27;s and then we get the standard form. And the reason the standard form is useful is because if you know how to graft X squared, then you see our expression over here will be a shift to the right because we&#x27;re subtracting too from the ex and then also here will shift down by nine and we could see that our vortex is the point too negative. Nine. So let&#x27;s go ahead and plot that point in. There&#x27;s two negative nine right down here. So there&#x27;s a rough sketch and then we know that and the regular graph of X squared. If you go over one unit from the Vertex, then the Y value goes up. I want so we&#x27;LL use that fact here. Let&#x27;s go over one unit. So here X equals one. Then we go up one unit to negative eight, and we can continue going in this fashion and so on. So from there and there&#x27;s a rough sketch just based on three points, you can get a better looking Graff if you want to plug in a few more points here. So, looking at the rough guess that I gave here, I&#x27;m guessing that the intercepts. So this is the guest. Let&#x27;s say X looks like about negative one half, and then maybe on this side, perhaps about X equals five. But we don&#x27;t have to guess, because now we can algebraic Lee confirm. So let&#x27;s do this in green. So here will use the quadratic formula. So we&#x27;LL have X equals negative B plus or minus, and then we have our square room B square minus four times a time. See and put that all over to a which is just too. So here I have four over to Celeste to and then plus or minus, and inside the radical will have sixteen plus twenty, so that will be two plus or minus. So radical thirty six is six. Divide that by two million three, and this is equal to either negative one or five. So these are our ex intercepts, and that&#x27;s your final answer.

Yuki Hotta · Answer

All right, let&#x27;s go ahead and solve this problem. So what we&#x27;re going to do is to try to graft to X over X minus one. Using a graphing calculator. Now you can. You are actually going to learn how to do this by hand. It&#x27;s not a difficult problem. However, it&#x27;s asking us to use a graphing device. A Let&#x27;s do it that way. All right, So what, You have to be careful if you&#x27;re writing it in the classical format, unlike where the fractions, You know where the numerator and the denominators are. If you have to write it like this, you need to make sure what the number is divided by it actually change the format so that you can plug it in exactly the way you want it to look like. Oh, so that&#x27;s good. I was about to say something else, but I&#x27;m going to refer to that later in. Yeah, All right. There you go. So two X over X minus one is going to look like that. And as you can see, there seems to be a line right there at two that these red lines are never going to touch. And let&#x27;s see if I can add another one. Can I do that? What can? So, let&#x27;s see. Let&#x27;s try X equals to 10 there you go. There&#x27;s going to be a vertical line right here that the red line is going to approach, but never going to touch. So you&#x27;re going to be able to figure out how to find out where these lines are, But that&#x27;s for another story. Anyhow, this is what you should expect to see in your graphing calculator. And let&#x27;s summarize it over here. There was one more thing I needed to mention E. If you see right here, you see that it goes through zero comma zero and that&#x27;s actually not a coincidence. This we can actually figure it out right now. So doing some of these by hand. If you let X equals to zero, why will end up being two times 0/0 minus one, which is, of course, zero. So we know that it passes through the origin. It seems like when why, equal to two, there was a line that the graph never touched. I also did X equals the one. So if you want to grab this thing by hand, it would look something like this. Okay, It&#x27;s a slanted hyper bola. And this is how you do these sort of problems, such

James Kiss · Answer

if we have or X plus three y equals 12 we find the X intercept by plugging zero in for wide, so four X equals 12. Therefore, X equals three is the X intercept. To find the Y intercept, we substitute 01 for acts unsolved or why, or John 00 and three wife was 12. Therefore, y equals or is the why.

Monique Rousselle Maynard · Answer

this item asks that you find the X and Y intercepts for the graph of function. Why eats for X minus X squared. Recall that the X intercept is that value of X one y zero and you&#x27;re why intercept is that value of zero? I&#x27;m sorry, that value of why when X equals zero. So let&#x27;s start with the X intercept. That&#x27;s it. Why equal to zero? And we need to solve this court. Roddick. I think the easiest way of the most efficient way to do this is to factor out, um, an ex. So I&#x27;m actually going to rewrite this burst in this form. Let&#x27;s factor on a negative X. So we&#x27;ll have X minus four and then using the zero product property, we would set both up these expressions both factors equal to zero. In here we would get that X equals zero or X equals four. So we have two possible ex intercepts here. The first is 00 The second is 40 in finding the why intercept. We substitute zero in every instance of X, and we see that why equal zero, which makes total sense because we had the X intercepted the origin as well

Heather Zimmers · Answer

for this equation, we&#x27;re going to do a variety of things. We&#x27;re going to start by finding the intercepts. And so for the X intercept, we substitute zero and for why we get X equals zero squared minus five. So X equals negative five. So that would be the point. Negative 50 And for the Y intercept, we substitute zero in for X. So we have zero equals y squared minus five. We can add five to both sides and then square root, and we get why equals plus or minus square root? Five. So we have to. Why intercepts? Zero square root five and zero negative square root five. For the symmetry tests. Let&#x27;s start with X axis symmetry and we can replace why, with the opposite of why and see if we get the equivalent equation. The opposite of Y scoop. The opposite of Y squared is the same as Y squared, so this is equivalent to the original equation, so that should say yes. Yes, we have X axis symmetry for a Y axis symmetry. We&#x27;re going to replace X with the opposite of X and see if this is equivalent to the original equation and Even if we multiply both sides by negative one, it&#x27;s not equivalent to the original. So no, there&#x27;s no Y axis symmetry and then, for origin symmetry. See if I can get that spelled correctly there. We&#x27;re going to replace both X and y with their opposites. So the opposite of X equals the opposite of why squared minus five and we can simplify the opposite of Y squared, as we did before. But still, this is not equivalent to the original, so there&#x27;s no origin symmetry. Okay, let&#x27;s plot the points we have. So we have negative 50 and then we have zero square root five, which is approximately 2.2 and then to your own negative square root 50 negative 2.2. We could expect this to look like a sideways parabola. It does have X axis symmetry, so we have something like this, and we could make a table of values and plug in more numbers to get more exact points to plot

Problem

In Exercises 59-64, use a graphing utility to gra…

Problem 58 Medium Difficulty

In Exercises 57 and 58, determine the x-intercept(s) of the graph visually. Then find the x-intercept(s) algebraically to confirm your results.

$ y = 2x^2 + 5x - 3 $

Answer

$\left(\frac{1}{2}, 0\right),(-3,0)$

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