<transcript><audio_0>okay here we have 9.6 graphing an absolute value equation of the form y equals a times the absolute value of x so some things that i want you to understand</transcript><caption><image_1>The image shows a whiteboard with a handwritten note on it. The note is written in black marker and appears to be a mathematical equation. The equation is written as "y = 0.1x1" and is written on the left side of the whiteboard. On the right side, there is a yellow calculator with a black screen and buttons. The calculator is placed next to the notebook. The background of the image is decorated with colorful flowers and leaves.</caption><video><caption><image_2>The image shows a person's hand holding a black marker and writing on a whiteboard. The whiteboard is open and there is a yellow calculator next to it. The person is writing on the whiteboard with black marker. The text on the board reads "9.6 Bracing an absolute value equation of y = 0.1x1". The background of the image is decorated with colorful flowers and a blackboard.</caption><caption><image_3>The image shows a person's hand holding a black pen and writing on a whiteboard. The whiteboard is attached to a blackboard with a colorful floral wallpaper in the background. On the right side of the image, there is a blue and yellow calculator. The person is using the calculator to write on the whiteboard, which appears to be a mathematical equation. The equation is written in black marker and is written on a piece of paper.</caption></video><transcript><audio_4>is that when you're drawing the absolute value of x it's important to know what that looks like so what does y equal the absolute value of x look like</transcript><transcript><audio_5>so when you plug in zero into this like if i were to make a chart and you plug in zero absolute value of zero is zero so that's this point here if you plug in negative one or positive one the absolute value of</transcript><transcript><audio_6>negative one and the absolute value of positive one are both positive one so i get this point here and this point here the same with negative two and positive two the absolute value of negative two and</transcript><transcript><audio_7>the absolute value of positive two are positive two so you end up with these points here and so what happens is it creates this v</transcript><transcript><audio_8>shape it's essentially a line but then all the negative values turn positive so that's why it goes upward like this so it should have been here and then because all the y values are non positive because of the absolute value it shifts</transcript> okay here we have 9.6 graphing an absolute value equation of the form y equals a times the absolute value of x so some things that i want you to understand is that when you're drawing the absolute value of x it's important to know what that looks like so what does y equal the absolute value of x look like so when you plug in zero into this like if i were to make a chart and you plug in zero absolute value of zero is zero so that's this point here if you plug in negative one or positive one the absolute value of negative one and the absolute value of positive one are both positive one so i get this point here and this point here the same with negative two and positive two the absolute value of negative two and the absolute value of positive two are positive two so you end up with these points here and so what happens is it creates this v shape it's essentially a line but then all the negative values turn positive so that's why it goes upward like this so it should have been here and then because all the y values are non positive because of the absolute value it shifts
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