00:00As you can see, we are given a parabolic graph of our y = fx function.
00:04According to this, he says you have drawn the graph of the absolute value of x.
00:07Now, before we move on to absolute values, I will write the equation for our parabola, given its graph.
00:15Now, friends, I'm asking what the equations were that were in the form fx equals a times x squared plus b times x plus c.
00:24Guys, the graph indicated a parabola, right?
00:27I could actually write it like this too.
00:29A times x minus x1 times x minus x2.
00:35Our A here, friends, what is it? It's positive. Arms pointing upwards.
00:39What are x1 and x2? They are the points where the x-axes intersect.
00:42Let's get started, everyone.
00:44Now I know that we can write our fx function here like this.
00:50A times x minus 2 times x minus 8.
00:57Friends, why was the number 16 given here?
01:00What is our F0 value, guys?
01:03She's 16.
01:05In this case, can I find 'a'?
01:07I'll find it.
01:07I'll put 0 in place of x.
01:08For x equals 0.
01:13f0 equals 16.
01:14That's equal to a times 0 minus 2, which is minus 2 times 0 minus 8, which is minus 8.
01:21That equals 16 multiplied by a equals 16.
01:25If I divide both sides by 16, we can find that 'a' is 1.
01:28If 'a' is one, then the equation of our function is actually this.
01:331 times x minus 2 times x minus 8.
01:37If this is the case, what is the absolute value of f as x?
01:44It equals absolute value x minus 2 times absolute value x minus 8.
01:51Right, guys?
01:53Yes.
01:53Now I know that
01:58x here, if it equals 0, then this is the place, right guys?
02:02In the absolute value function, this is our function.
02:05x1 equals 2.
02:08x2 could be equal to minus 2.
02:10Here, x1 equals 8.
02:13x2 equals.
02:15Let me write it like this.
02:16x2 could be equal to minus 8.
02:18Right, guys?
02:19So what does this mean?
02:22Now, let's look at the graph.
02:24Showing it from a graph makes more sense.
02:31There are 16 here, right guys?
02:35The graph of our function in sections 2 and 8.
02:38Here, friends, while cutting, x 80
02:43In absolute terms, what are friends?
02:46-2 and -8 reset this place to zero, folks.
02:52Isn't it?
02:52I found it here.
02:53Okay then, it will pass through here.
02:55But friends, you could also write F1 here.
03:00f's absolute value will be equal to 1, which is equal to f's absolute value will be equal to -1.
03:08It will give the same value.
03:09And at the same time, I'm assigning the absolute value of f to 2.
03:14Right, guys?
03:15Let's even say 3 here.
03:17Because 2 also resets it.
03:18What does "f absolute value equals 3" mean, friends?
03:22The absolute value of f minus 3 will give the same value.
03:25Do you know what this means?
03:26y will cut the same place.
03:27So what happens to friends when this happens?
03:29That's the point I'm trying to make.
03:30y has the same value, because the function gives the same value.
03:33over there
03:38received in this way
03:40We will buy it.
03:41How relative to the y-axis?
03:42if the absolute value of f(x)
03:45How were we doing it, guys?
03:46What were we doing with respect to that negative axis?
03:48The remaining bottom piece
03:49We were carrying it on top, we were getting symmetry.
03:51Do the same with this.
03:52When the absolute value is y, then
03:54So if f is the absolute value of x
03:56What are we going to do, guys?
03:58relative to the y-axis, that relative to the y-axis
03:59We'll take this side as symmetry.
04:01We won't touch the bottom part.
04:03Maybe from here, friends.
04:04Now look
04:07in this way
04:09Let's imagine this as a parabola.
04:11Let's think of this as a parabola, folks.
04:13Likewise
04:14What exactly is this?
04:16y equals
04:17f is the absolute value of our x.
04:21This is a graph, folks.
04:22Look
04:23the area he acquired here
04:25Friends
04:25x equals 1
04:26x equals
04:27It gets it at minus 1.
04:28x equals
04:29I'm just throwing it away.
04:30It was already resetting at -2.
04:33minus 2/3
04:34It takes 2/3 of the amount.
04:35The graph of the same function
04:37friends who will receive it.
04:38Because
04:39y equals
04:40f is the absolute value of our x.
04:41graph
04:42relative to the y-axis
04:43after symmetry is obtained
04:45This is how it's drawn.
04:46He gets it in 3.
04:46He gets it at 4.
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