color(blue)("Tip 1: Shape of the graph")Tip 1: Shape of the graph
If an absolute is positive we get the shape vvv⋁
If an absolute is negative we get the shape ^^^color(red)( larr" Our one")⋀← Our one
This follows the same pattern as with a quadratic.
If the x^2x2 term is positive we get uuu⋃
If the x^2x2 term is negative we get nnn⋂
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color(blue)("Tip 2: horizontal position")Tip 2: horizontal position
If you add a value to the xx then it moves the graph left
If you subtract a value from the xx then it moves the graph right
Example: suppose we had say
y=x^2+2x-2y=x2+2x−2
then we dicide to change it so that we add 4 to xx. We have:
y=(x+4)^2+2(x+4)-2y=(x+4)2+2(x+4)−2
Because we have added 4 it moves the graph y=x^2_2x-2y=x2_2x−2 left by 4
color(red)("Our one:")Our one:
So if we add 10 to y=-|x|y=−|x| giving y=-|x+10|y=−|x+10| we move the graph of y=-|x|y=−|x| left by 10
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color(blue)("Tip 3: x-intercept")Tip 3: x-intercept
The graph crosses the x-axis at y=0y=0
y=-|x+10| color(white)("d")-> color(white)("d") 0=-|x-10|y=−|x+10|d→d0=−|x−10|
The only way we can obtain 0 as the value of yy is if x=+10x=+10
So we have: x_("intercept")->(x,y)=(10,0)xintercept→(x,y)=(10,0)
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color(blue)("Tip 4: y-intercept")Tip 4: y-intercept
The graph crosses the y-axis at x=0x=0
y=-|0+10| = -10y=−|0+10|=−10
So we have: y_("intercept")->(x,y)=(0,-10)yintercept→(x,y)=(0,−10)
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color(blue)("Tip 4: The vertex")Tip 4: The vertex
This occurs when the overall value color(red)("within")within the absolute is about to 'flip' sign from positive to negative. That is, it becomes 0 which happens at x=-10x=−10
y=-|color(magenta)(x)+10|y=−|x+10|
color(limegreen)(y)=-|ubrace(color(magenta)(-10)+10)| = color(limegreen)(0)
color(white)("ddddddddd")darr
color(white)("dddddddd.d")0
Vertex ->(x,y)=(color(magenta)(-10),color(limegreen)(0))
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