Question

How do you graph `y=-abs(x-1/2)-14`?

Answer 1

Reflected over the `x`-axis and translated `1/2` to the right and `14` down.

Explanation:

graph{-|x-1/2|-14 [-41.15, 39.95, -24.95, 15.58]}

The parent function of the function you are trying to graph is `y = |x|`

graph{|x| [-10, 10, -5, 5]}

The function that you are graphing is just a reflection and translation of the parent function.

The standard form of an absolute value function is `f(x) = a|x-h|+k`.

As the function you are trying to graph is also in standard form, it is very simple to graph. Because the coefficient `(a)` is a negative number, a `-1` in this case, you know that you must reflect over the `x`-axis.

Then you must translate the function as specified. The `(k)` value changes the vertex of the function by moving it up or down, and `(h)` left or right. The `(k)` value is `-14`, so you move `14` units down, and the `(h)` value is `-1/2` so you move the vertex `1/2` units to the right.

*It is important to note that for all transformations of parent functions, you must do any reflections, compression and or stretching before you do any translations or you will end up graphing the equation incorrectly.

Khan Academy link