Question

Sketch the graph: y=|x+1|-2
Just need some guidance! Thanks!

Answer 1

Ok, well lets start with what you know..

How would you graph y=|x| ?

Answer 2

y=|x+1|-2

To find the x-intercept, substitute in 0 for y and solve for x.
(0)=|x+1|-2

Since x is on the right-hand side of the equation, switch the sides so it is on the left-hand side of the equation.
|x+1|-2=(0)

Remove the parentheses around the expression 0.
|x+1|-2=0

Since -2 does not contain the variable to solve for, move it to the right-hand side of the equation by adding 2 to both sides.
|x+1|=2

Remove the absolute value term. This creates a \ on the right-hand side of the equation because |x|=\x.
x+1=\(2)

Set up the + portion of the \ solution.
x+1=2

Move all terms not containing x to the right-hand side of the equation.
x=1

Set up the - portion of the \ solution.
x+1=-(2)

Multiply -1 by the 2 inside the parentheses.
x+1=-2

Since 1 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 1 from both sides.
x=-1-2

Subtract 2 from -1 to get -3.
x=-3

The solution to the equation includes both the positive and negative portions of the solution.
x=1,-3

To find the y-intercept, substitute in 0 for x and solve for y.
y=|(0)+1|-2

Remove the parentheses around the expression 0.
y=|0+1|-2

Combine all similar expressions.
y=|1|-2

The absolute value of 1 is 1, so the absolute value symbols can be removed.
y=1-2

Solve the equation.
y=-1

These are the x and y intercepts of the equation y=|x+1|-2.
x=1,-3, y=-1