# Graph y=-|x+7|+3 y=-|x+7|+3
Find the absolute value vertex. In this case, the vertex for y=-|x+7|+3 is (-7,3).
To find the x coordinate of the vertex, set the inside of the absolute value x+7 equal to 0. In this case, x+7=0.
x+7=0
Subtract 7 from both sides of the equation.
x=-7
Replace the variable x with -7 in the expression.
y=-|(-7)+7|+3
Simplify -|(-7)+7|+3.
Simplify each term.
y=-|0|+3
The absolute value is the distance between a number and zero. The distance between 0 and 0 is 0.
y=-0+3
Multiply -1 by 0.
y=0+3
y=0+3
y=3
y=3
The absolute value vertex is (-7,3).
(-7,3)
(-7,3)
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 -9 into f(x)=-|x+7|+3. In this case, the point is (-9,1).
Replace the variable x with -9 in the expression.
f(-9)=-|(-9)+7|+3
Simplify the result.
Simplify each term.
f(-9)=-|-2|+3
The absolute value is the distance between a number and zero. The distance between -2 and 0 is 2.
f(-9)=-1⋅2+3
Multiply -1 by 2.
f(-9)=-2+3
f(-9)=-2+3
f(-9)=1
y=1
y=1
y=1
Substitute the x value -8 into f(x)=-|x+7|+3. In this case, the point is (-8,2).
Replace the variable x with -8 in the expression.
f(-8)=-|(-8)+7|+3
Simplify the result.
Simplify each term.
f(-8)=-|-1|+3
The absolute value is the distance between a number and zero. The distance between -1 and 0 is 1.
f(-8)=-1⋅1+3
Multiply -1 by 1.
f(-8)=-1+3
f(-8)=-1+3
f(-8)=2
y=2
y=2
y=2
Substitute the x value -5 into f(x)=-|x+7|+3. In this case, the point is (-5,1).
Replace the variable x with -5 in the expression.
f(-5)=-|(-5)+7|+3
Simplify the result.
Simplify each term.
f(-5)=-|2|+3
The absolute value is the distance between a number and zero. The distance between 0 and 2 is 2.
f(-5)=-1⋅2+3
Multiply -1 by 2.
f(-5)=-2+3
f(-5)=-2+3
f(-5)=1
y=1
y=1
y=1
The absolute value can be graphed using the points around the vertex (-7,3),(-9,1),(-8,2),(-6,2),(-5,1)
xy-91-82-73-62-51
xy-91-82-73-62-51
Graph y=-|x+7|+3     