# Finding X and Y intercepts in an absolute value equation.

#### Toxxic Kitty

##### New member
I hope this is in the correct forum. I'm currently enrolled in college algebra, but it's been 6 - 7 years since I've seen many of these types of equations. I really need step by step help and the reasons behind why I'm doing said steps.

Determine the x and y intercepts for the given function:

K(x) = -|x| + 2

#### Subhotosh Khan

##### Super Moderator
Staff member
I hope this is in the correct forum. I'm currently enrolled in college algebra, but it's been 6 - 7 years since I've seen many of these types of equations. I really need step by step help and the reasons behind why I'm doing said steps.

Determine the x and y intercepts for the given function:

K(x) = -|x| + 2
For that, you need face-2-face classroom help.

My first suggestion would be - plot the function in the domain [-5,5]. I assume you know how to do that.

What do you see? Where does the function cross the x-axis? Where does the function cross the y-axis?

#### stapel

##### Super Moderator
Staff member
I'm currently enrolled in college algebra, but it's been 6 - 7 years since I've seen many of these types of equations.
That's why they had you take a placement test: so that they could "place" you in the class which is best for your current level of skill, being what you remember.

I really need step by step help and the reasons behind why I'm doing said steps.

Determine the x and y intercepts for the given function:

K(x) = -|x| + 2[/QUOTE]
To review what it means to "find intercepts", try (this) online refresher course. To review how to solve absolute-value equations, try (here). Once you've gotten yourself back up to speed, follow the instructions given in the lessons:

For the y-intercept, set x equal to zero and solve. (Well, just simplify, in this case.)

For the x-intercept, set y equal to zero and solve.

If you get stuck, please reply showing all of your efforts so far. Thank you!

#### Toxxic Kitty

##### New member
That's why they had you take a placement test: so that they could "place" you in the class which is best for your current level of skill, being what you remember.

For whatever reason, even though I have not been in college since 2011, they did not have me take a placement test. I've tried to make it to the tutoring center on campus, but seeing as how I work 40+ hours a week Monday - Friday my schedule doesn't allow me to get to the tutoring center during business hours. I really appreciate you posting those links. They helped a lot.

So far I have:

Determine the x and y intercepts for the given function:

K(x) = -|x| + 2

K(x)= -|x| + 2
K(0)= -|0| + 2
K(0) = 0+2
k(0) = 2
Y-intercept is (0,2)?

Determine the x and y intercepts for the given function:

K(x) = -|x| + 2

0 = -|x| + 2
0 - 2 = -|x| + 2- 2
-2/-1=K(x) = -|x|/-1
2 = x
x-intercept is (-2,0) and (2,0)?

#### stapel

##### Super Moderator
Staff member
For whatever reason, even though I have not been in college since 2011, they did not have me take a placement test.
Oh, dear. I'm very sorry to hear that. It's very irresponsible of them. Placement tests are intended to avoid just exactly the problem you've encountered: taking a class for which you're smart enough, but for which you're not sufficiently prepared. You have my sympathies.

So far I have:

Determine the x and y intercepts for the given function:

K(x) = -|x| + 2

K(x)= -|x| + 2
K(0)= -|0| + 2
K(0) = 0+2
k(0) = 2
Y-intercept is (0,2)?
Correct.

Determine the x and y intercepts for the given function:

K(x) = -|x| + 2

0 = -|x| + 2
0 - 2 = -|x| + 2- 2
-2/-1=K(x) = -|x|/-1
You're good to the above line. But...

...how did you get this?

x-intercept is (-2,0) and (2,0)?
And then how did you arrive here?

Instead, think about what the absolute value is and means. (here) If |x| = 2, then this means that x is two units from zero. It does not mean that x must be two units to the right of zero. It could also be two units to the left. This is the source of the other x-intercept.

Note: You can confirm the intercepts by looking at the graph. (here and here)

#### Toxxic Kitty

##### New member
Determine the x and y intercepts for the given function:

K(x) = -|x| + 2

0 = -|x| + 2
0 - 2 = -|x| + 2- 2

Okay, so I got this far. Now would you Divide by the negative to get x by itself? Or, since it is possible to solve this, -|x|, you would leave it alone and get:

-2 = -|x|?

Because based on the article, assuming x = -2 , you can solve this K(x) = -|x| as K(x) = -|2|. So you would write K(x) = -(-2), so either way the x-intercept would be positive. This means the x-intercept is (2,0)?

#### ksdhart

##### Full Member
Determine the x and y intercepts for the given function:

K(x) = -|x| + 2

0 = -|x| + 2
0 - 2 = -|x| + 2- 2

Okay, so I got this far. Now would you Divide by the negative to get x by itself? Or, since it is possible to solve this, -|x|, you would leave it alone and get:

-2 = -|x|?

Because based on the article, assuming x = -2 , you can solve this K(x) = -|x| as K(x) = -|2|. So you would write K(x) = -(-2), so either way the x-intercept would be positive. This means the x-intercept is (2,0)?
I'm a little confused as to what you're doing here. You say "assuming x = -2, you can solve this K(x) = -|x| as K(x) = -|2|". Why are you saying that K(x) = -|x|? If that were true, then according to your steps above, K(x) would have to be -2. But when finding x-intercepts, your goal is to find values of x when y is 0. You're graphing the function, so the output of the function is the y-coordinates. I sometimes find it helpful to begin the entire process with a step like this:

K(x) = y = -|x| + 2

Since K(x) = y, and we know y is 0 at the x-intercepts, then K(x) must also be 0 at those intercepts. And setting K(x) to 0 is what you did at the start of your work, which was correct. In fact, all of your work up to the last line where you say -2 = -|x| is fine. Now, if you graph the function, you can see that it crosses the x-axis twice. So you know you'll have two x-intercepts. Those x-values can be found by solving the equation:

-2 = -|x|
2 = |x| (Divide both sides by -1)

So, to rephrase what Stapel said in his previous post... if the absolute value of x is 2, then what are the possible values of x? Those are your x-intercepts.

#### Toxxic Kitty

##### New member
I'm a little confused as to what you're doing here. You say "assuming x = -2, you can solve this K(x) = -|x| as K(x) = -|2|". Why are you saying that K(x) = -|x|? If that were true, then according to your steps above, K(x) would have to be -2. But when finding x-intercepts, your goal is to find values of x when y is 0. You're graphing the function, so the output of the function is the y-coordinates. I sometimes find it helpful to begin the entire process with a step like this:

K(x) = y = -|x| + 2

Since K(x) = y, and we know y is 0 at the x-intercepts, then K(x) must also be 0 at those intercepts. And setting K(x) to 0 is what you did at the start of your work, which was correct. In fact, all of your work up to the last line where you say -2 = -|x| is fine. Now, if you graph the function, you can see that it crosses the x-axis twice. So you know you'll have two x-intercepts. Those x-values can be found by solving the equation:

-2 = -|x|
2 = |x| (Divide both sides by -1)

So, to rephrase what Stapel said in his previous post... if the absolute value of x is 2, then what are the possible values of x? Those are your x-intercepts.
I had initially thought that since the number contained with in the absolute value symbols could be either positive or negative, that my answer would be both (2, 0) and (-2, 0). But, Stapel said that was incorrect, so I tried to think of what else it could be.