# Graph y=-|x+4|+4

y=-|x+4|+4
Find the absolute value vertex. In this case, the vertex for y=-|x+4|+4 is (-4,4).
To find the x coordinate of the vertex, set the inside of the absolute value x+4 equal to 0. In this case, x+4=0.
x+4=0
Subtract 4 from both sides of the equation.
x=-4
Replace the variable x with -4 in the expression.
y=-|(-4)+4|+4
Simplify -|(-4)+4|+4.
Simplify each term.
y=-|0|+4
The absolute value is the distance between a number and zero. The distance between 0 and 0 is 0.
y=-0+4
Multiply -1 by 0.
y=0+4
y=0+4
y=4
y=4
The absolute value vertex is (-4,4).
(-4,4)
(-4,4)
The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.
Interval Notation:
(-∞,∞)
Set-Builder Notation:
{x|x∈ℝ}
For each x value, there is one y value. Select few x values from the domain. It would be more useful to select the values so that they are around the x value of the absolute value vertex.
Substitute the x value -6 into f(x)=-|x+4|+4. In this case, the point is (-6,2).
Replace the variable x with -6 in the expression.
f(-6)=-|(-6)+4|+4
Simplify the result.
Simplify each term.
f(-6)=-|-2|+4
The absolute value is the distance between a number and zero. The distance between -2 and 0 is 2.
f(-6)=-1⋅2+4
Multiply -1 by 2.
f(-6)=-2+4
f(-6)=-2+4
f(-6)=2
y=2
y=2
y=2
Substitute the x value -5 into f(x)=-|x+4|+4. In this case, the point is (-5,3).
Replace the variable x with -5 in the expression.
f(-5)=-|(-5)+4|+4
Simplify the result.
Simplify each term.
f(-5)=-|-1|+4
The absolute value is the distance between a number and zero. The distance between -1 and 0 is 1.
f(-5)=-1⋅1+4
Multiply -1 by 1.
f(-5)=-1+4
f(-5)=-1+4
f(-5)=3
y=3
y=3
y=3
Substitute the x value -2 into f(x)=-|x+4|+4. In this case, the point is (-2,2).
Replace the variable x with -2 in the expression.
f(-2)=-|(-2)+4|+4
Simplify the result.
Simplify each term.
f(-2)=-|2|+4
The absolute value is the distance between a number and zero. The distance between 0 and 2 is 2.
f(-2)=-1⋅2+4
Multiply -1 by 2.
f(-2)=-2+4
f(-2)=-2+4
f(-2)=2
y=2
y=2
y=2
The absolute value can be graphed using the points around the vertex (-4,4),(-6,2),(-5,3),(-3,3),(-2,2)
xy-62-53-44-33-22
xy-62-53-44-33-22
Graph y=-|x+4|+4

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