00:00Draw the graph of the function f(x) equals x squared plus x minus 12, of absolute degree.
00:05Now, friends, I know I'd like to share a little anecdote.
00:10What do quadratic equations of the form a times x squared plus v times x plus c equals 0 form?
00:18Friends?
00:19It forms a parabola, right?
00:21Okay guys, I want to briefly explain this before getting into the topic completely, because it's related to absolute value and comes up a lot.
00:27Therefore, I'll be back a little bit.
00:30Now, friends, here's all the information we need.
00:34If our network is positive, as you can see here, the arms of our parabola's graph will point upwards.
00:47If A is less than 0, the arms point downwards.
00:53You can even eliminate some options from here, you can get rid of some questions in exams.
00:58Now, friends, when I get to this point, since it also represents a parabola, it has a peak point.
01:06What is the peak point?
01:07R is represented as k.
01:10Our R is here, folks.
01:14It is taken as minus b divided by 2 times a.
01:17If your K is F, then your F is R.
01:24Let's be aware of this too.
01:25Let's start by constructing our parabola so we can later graph its absolute value.
01:30Friends, to create the graph of our parabola, let's first write Fx equals x squared plus x minus 12.
01:39Can we separate this from the multiplier?
01:40Let's separate them. x to x
01:424 to 3
01:43Right, guys?
01:45They all satisfy each other in terms of x.
01:46Friends, I'll write it like this.
01:48x to x multiplied by 3
01:50x to 4
01:52Now I am here
01:54If I give x equals 0
01:58cut y
01:59y-axis
02:00y ordinate point
02:03friends he cut off
02:04I'll find the point. For x equals 0.
02:08our
02:09It comes out to minus 12.
02:10If y equals 0, then...
02:12There are 2 values. x-axis
02:14Right? So what happens then, guys?
02:16x minus 3 times
02:19x plus 4 equals 0
02:21x 1 equals 3
02:22and x 2 equals
02:24It comes out to minus 4.
02:27Now, friends...
02:28Let's take a look at the peak.
02:31If it were a perfect square, our job would be easy, but...
02:32Now we need the peak.
02:34t, r to k
02:36Our r was minus b divided by 2a.
02:38isn't it?
02:39Oh, by the way, friends...
02:40Since our 'a' is greater than 0
02:42Arms will be pointing upwards.
02:43Is point A not 1?
02:46So, since it's a positive number...
02:48r minus b divided by 2a
02:49Friends, what does -b mean here?
02:51minus 1
02:53part 2
02:56From where?
02:57Our r is here too.
02:58Our b is also 1.
02:59Our 'a' is also 1.
03:00It makes minus 1 divided by 2.
03:01According to our rules.
03:02So what is f r?
03:04So, f minus 1 divided by 2
03:07It equals.
03:09k value
03:09It equals.
03:10I'm taking this place, guys.
03:12One second.
03:13f minus 1 divided by 2
03:14It equals.
03:16Friends
03:16What will we do instead of x?
03:18We'll add minus 1 divided by 2.
03:19What is the square of -1 divided by 2?
03:201/4
03:21minus 1 divided by 2
03:23minus 12
03:24I'll equalize the denominators immediately.
03:274
03:281 minus 2 minus 48
03:31Right, guys?
03:33section 4
03:33What is that equal to?
03:35minus 50
03:35It's minus 49 divided by 4.
03:38What is this?
03:39What happened to our peak value, guys?
03:41in this situation?
03:42I'll write it here too.
03:43minus 49 divided by 4
03:46our
03:47minus 1 divided by 2
03:49x, that is
03:50x point
03:51Here
03:52Our y is
03:52minus 49 divided by 4
03:55minus 1 divided by 2
03:57minus 49 divided by 4
03:57right now
04:00I'll move on to our graph.
04:02Our x was intersecting at the same point, guys.
04:04And what was our y?
04:05Our y was minus 12
04:07Right, guys?
04:09our x
04:09minus 4 to 3
04:11I'm placing them halfway in their positions right away.
04:18Our peak point is, friends.
04:21arms will point upwards
04:22isn't it?
04:23Yes
04:23our
04:24It will go from minus 12.
04:26And
04:27this peak value point
04:28I want to write something, friends.
04:29with your permission
04:30The peak is here.
04:31our x
04:34minus 1 divided by 2
04:36our place
04:36minus 49 divided by 4
04:43It seems to reach its highest value here.
04:45ours
04:46What are we friends for?
04:47Of course, our function
04:49Friends
04:50This is how it will be
04:53I'll draw a lot, but...
04:55I don't know how to do it.
04:57I drew badly.
04:58y equals
04:59minus 12
05:00By the way, what is the score here, guys?
05:01minus 49 divided by 4
05:02minus 12 point something
05:04-12 somewhere around here
05:09Yes
05:09Now that you've arrived, friends
05:11here
05:12I'm coming from here
05:14arms up
05:16Yes
05:18Like this
05:18instead of 3 here
05:20Please accept this section as number 3.
05:21When I draw this, my friends
05:23This is the peak point.
05:24t, r, y, k
05:26passed through here
05:28And this is
05:29What's up, guys?
05:30equals y
05:31fx
05:32why?
05:33graph of the function
05:34Okay, but how do I draw this instead of an absolute value?
05:38Of course, these friends
05:39the part that lies under the x-axis
05:41What am I going to do?
05:42relative to the x-axis
05:43I will get the symmetry
05:45And I'll draw it above.
05:46Let's take a look at that too.
05:47Hopefully I'll draw it more neatly here.
05:52Friends
05:53It comes this far.
05:54Is it ok?
05:55minus 4
05:57It's coming from over there.
05:58Because these places are positive.
06:00equals y
06:02absolute value
06:03fx
06:04Ok
06:05Now, friends...
06:07after arriving here
06:08And here's number 3
06:08minus 49 divided by 4
06:11minus 1 divided by 2
06:13I'll say I'll get it from here.
06:14if this is minus 1 divided by 2
06:16If this part is 49 divided by 4
06:21I'm getting its symmetry, you know.
06:22this place too
06:23I'll get its symmetry here.
06:25What am I going to do, guys?
06:27I will combine them here
06:28my peak
06:29This is my new peak now.
06:31and also
06:33y is equal to the value of x 12.
06:35I'll bring my friends here.
06:38Let's also write x 12.
06:40So, this is what happened, guys.
06:45Yes
06:46Here's the new one
06:48absolute value of y
06:49FX chart, friends.
06:51That's how it happened
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