How can you write an absolute value equation so that the vertex will be at (-5,-7)?

Answer 1

The obvious answer to me would be y = |x + 5| - 7

The parent function, |x|, has vertex at (0, 0).

The + 5 moves 5 to the left, and the -7 moves down 7.

Answer 2

The absolute value function, y = |x|, forms a "V" with the vertex at (0,0). This means that |0| is 0.

The goal is to have the vertex at (-5,-7), so the function must look like y = |z| - 7

Now that we have the shift in the y-direction, we mus find z.

To do that, we must add 5 to make up for the (-5):

y = |x+5| - 7

Check:

What is y when x=-5?

y = |-5+5| - 7

y = -7 o.k.