Question

How do you find the x intercept of `y = -|x+10|`?

Answer 1

The x intercept of a function always occurs when y = 0. Therefore, we must solve the equation for x.

Explanation:

`0 = -|x + 10|`

When solving an absolute value equation, you must consider two scenarios.

a) The absolute value is positive

`0 = -x - 10`

`10 = -x`

`-10 = x`

b) The absolute value is negative

`0 = -(-(x + 10)))`

`0 = -(-x - 10)`

`0 = x + 10`

`-10 = x`

So, there is only 1 x intercept in this case. Here is a graph of your function:

graph{y = -|x + 10| [-20.27, 20.28, -10.14, 10.13]}

However, we must always check. In many cases, there will be more than one x intercept.

Example:

Find the x intercept(s) of `y = |2x + 6| - 4`.

a) The absolute value is `color(red)(+)`:

`0 = 2x + 6 - 4`

`-2 = 2x`

`-1 = x`

b) The absolute value is `color(blue)(-)`

`0 = -(2x + 6) - 4`

`4 = -2x - 6`

`10 = -2x`

`-5 = x`

Thus, we have two x intercepts: `(-1, 0) and (-5, 0)`, as shows the graph of that function.

graph{y = |2x + 6| - 4 [-20.27, 20.28, -10.14, 10.13]}

Practice exercises:

1. Indicate all the x intercepts of the functions below.

a) `y = |-2x + 7|`

b) `y = |3x - 4| - 3`

c) `y = |5x + 1| + 2x`

Good luck!