For Alg 2 help--I need help finding an absolute value equation

[Punstermeister]

I would like to ask for help in finding an absolute value equation for the following coordinates, I would appreciate any help for not only an answer but also the reasoning behind the answer. Thank you.

a. (0,0) (1,-3) (-1,-3)

b. (0,0) (2,1) (-2,1)

c. (0,0) (-2,-1) (2,-1) (-4,0) (-6,2)

I have tried to use the general formula for f(x) = a/x-h/-k but am finding difficulities

 

[tkhunny]

I really cannot understand the problem statement. Can you provide a worked example?

 

[lookagain]

I would like to ask for help in finding an
absolute value equation for the following coordinates,...

a. (0,0) (1,-3) (-1,-3)

y = f(x) = a|x-h| + k ** but am finding difficulities

** I want to use this form, where (h, k) is the coordinates of the vertex.

The points (1, -3) and (-1, -3) lie on a line parallel to the x-axis,
which is y = -3. The average of their x-coordinates is x = 0.
So, the vertex is (0, 0), and it is the maximum point. So h = k = 0.

The form is now simplified from f(x) = a|x - 0| + 0
to f(x) = a|x|.

Plug in either (1, -3) or (-1, -3). I'll use the first one:

-3 = a|1|

-3 = a

a = -3

\(\displaystyle So \ the \ equation \ is \ f(x) = -3|x|.}\)




The second two points lie below the vertex so that the variable a
is negative. The vertex is at the origin so h = k = 0.





Then the equation of this function is of the form:

f(x) = a|x| + k.

 

[tkhunny]

Ah. There it is. Please use "/" only for division. Find the vertical one "|" for absolute value.