how do you graph y = -|x - 3| - 4,, y = |x - 3| - 4,, y= -2 |x + 3|-4,, and y = 2 |x + 3| - 4 im confused?
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The answer is to graph one of them at a time :)
Here is how to graph the first one
First notice the point (x,y) = (3, -4) is a vertex so graph that.
Then I would pick a few other easy values of x.
It helps if you know that the graph is going to be two different rays in the plane (which is a line that starts at a particular point which is (3,-4) in this case, and then goes off to infinity in a straight constant direction, but not in the opposite direction at all. So it has two different directions, one with slope +1 and one with slope -1. But that isn't the whole complete answer because that could be 4 different directions and only 2 will actually be part of the answer.)
x=0 -> y= -|-3| - 4
You have to know |-3| = 3
y = -3 -4 = -7
so one line has (3,-4) and (0,-7) on it. The slope is 1 since x and y both change by -3
Then try x=5
x=5 -> y = -|2| - 4 = -6
so the other line has (3,-4) and (5,-6) on it. The slope is -1 since x changed by +2 and y changed by -2
A good pattern to realize is that a term with +|x + c| for some constant c will have the shape of a V and if it has -|x+c| it will have an upside-down V.
If you are feeling lazy and do not want to do your math or learn about absolute values or make your own plots or succeed in life at all, or want to see the right answer, try this link:
http://www.wolframalpha.com/input/?i=-|x…
The Wolfram Alpha engine will graph it nicely for you.
Here is how to graph the first one
First notice the point (x,y) = (3, -4) is a vertex so graph that.
Then I would pick a few other easy values of x.
It helps if you know that the graph is going to be two different rays in the plane (which is a line that starts at a particular point which is (3,-4) in this case, and then goes off to infinity in a straight constant direction, but not in the opposite direction at all. So it has two different directions, one with slope +1 and one with slope -1. But that isn't the whole complete answer because that could be 4 different directions and only 2 will actually be part of the answer.)
x=0 -> y= -|-3| - 4
You have to know |-3| = 3
y = -3 -4 = -7
so one line has (3,-4) and (0,-7) on it. The slope is 1 since x and y both change by -3
Then try x=5
x=5 -> y = -|2| - 4 = -6
so the other line has (3,-4) and (5,-6) on it. The slope is -1 since x changed by +2 and y changed by -2
A good pattern to realize is that a term with +|x + c| for some constant c will have the shape of a V and if it has -|x+c| it will have an upside-down V.
If you are feeling lazy and do not want to do your math or learn about absolute values or make your own plots or succeed in life at all, or want to see the right answer, try this link:
http://www.wolframalpha.com/input/?i=-|x…
The Wolfram Alpha engine will graph it nicely for you.