Question

Write the formula for absolute value function if its graph has the vertex at point ( 1/3 ,−3) and passes through the point (1,1).

Answer 1

y=|6x-2|-3

Explanation:

I can see y=|x-1/3|-3 is a tempting answer, it does have its vertex at (1/3,-3) but it doesn't go through (1,1). This graph needs to be steeper, so we need to multiply x and the -1/3 coefficient next to it.

We multiply x and -1/3 each by 6, and boom! The graph goes through (1,1) and the vertex is still maintained at (1/3,-3) The -3 outside of the function doesn't change because the vertex's y-coordinate is -3, so it must stay the same.