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In $9-14 :$ a Sketch the graph of each function. b. From the graph, estimate the roots of the function to the nearest tenth. c. Find the exact irrational roots in simplest radical form.$$f(x)=x^{2}-10 x+18$$

a) graphb) The roots of $f$ ROUNDED TO THE NEAREST TENTH are the $x=2.4$ and $x=7.6$ as shown in the pic.c) $x=5+\sqrt{7}$ and $x=5-\sqrt{7}$

Algebra

Chapter 5

QUADRATIC FUNCTIONS AND COMPLEX NUMBERS

Section 1

Real Roots of a Quadratic Equation

Equations and Inequalities

Quadratic Functions

Complex Numbers

Polynomials

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Lectures

01:32

In mathematics, the absolu…

01:11

04:00

In $9-14 :$ a Sketch the g…

08:40

03:58

03:56

05:45

00:46

In $9-14$ : a. For each gi…

00:39

01:40

00:26

All right, so here we have the function X squared minus 10 X plus 18 and we are shown base a graph. We have to sketch the career here now, So let's start up a And if we analyze this coefficient of the eight terms or one, you know it's gonna open up and our Vertex to start off with will be. But again, that X equals negative b over to a formula, which is 10 over to just wait or sorry, five ages 10 minus two. So, yeah. Um, no. I have to find the white corn it at five. Peoples 25 minus 50 plus 18 which is Meggett to 25 plus a team, which is just a negative seven. So the Vertex just five negative seven and I doubled up the y scale here to account for the larger numbers here. So be a little easier for us to do that. And let's also thinks our ex killer ate here because Arbor, Texas, five cents will be able to do numbers on the right side. Most we fix it, so let's make are right side over here at 10. In her left side. Uh, zero. So we go back to what we get. Five negative. Seven of the pretext. It's a negative. Seven will be around right over here. But the critics was started by the numbers around it. F of six equals 36 minus 60 plus 18. That's six, if of four equals 16 minus 40. Native 24. That is closely team once again. Negative six. What about the ***? Right there. Um, put it in. I'm not inside. Let's move on. F of seven equals 49 minus 70. Negative 21 plus 18 which is in negative three. Same thing for the other. Side nine minus 31 Because it in committee three. So right here will be negative. Three. We still have to get above that on XX, sis, so we can actually do part B. So we have to keep chugging along with these coordinates plotting. So let's try out eight and two, right? 64. Mine's a *** 16 plus 18. And we finally got to the positive side for minus 40. All right. Minus 20. That is you, um, 16 plus 18 which is to So I got a two on either side right here, and let's plot. And after we stay, catch this out. We have two points here. These points are gonna end up being useful for part because now we have to estimate the roots of the graph. And when we estimate we aren't actually finding the exact routes that is, we're trying to find something that's within the range of I would say it, like two or three tents would be good enough, since parting is inexact science. So let's see what we end up with we get. This is probably around. I so remember that we have, ah five in the middle, so we have seven points. Call that 7.8 with reasonable reasons. A 7.8 zero on the right side and then or three So should be a two point to North Side would be also pretty reasonable. So roots X equals to put two and seven point eats part. See, we actually have to find those roots and we go back to the quadratic formula to find the exact radical for it. So X equals negative B plus or minus the root of B squared minus for a c oh, over to A and we end up with 10 plus and minus the route of 100 minus four times 18 four times 18 72. So it's 100 minus 72 all over. Two times lunches, too. She So that's 10 plus or minus the roots of 28 over to we can simplify that radical. Route 28 is the same thing as true. Seven not equals five plus or minus. Oh, my clear five plus and minus Route seven and that is it.

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