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

Apr 3, 2016

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)))

$0 = - \left(- x - 10\right)$

$0 = x + 10$

$- 10 = x$

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 $y = | 2 x + 6 | - 4$.

a) The absolute value is $\textcolor{red}{+}$:

$0 = 2 x + 6 - 4$

$- 2 = 2 x$

$- 1 = x$

b) The absolute value is $\textcolor{b l u e}{-}$

$0 = - \left(2 x + 6\right) - 4$

$4 = - 2 x - 6$

$10 = - 2 x$

$- 5 = x$

Thus, we have two x intercepts: $\left(- 1 , 0\right) \mathmr{and} \left(- 5 , 0\right)$, 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) $y = | - 2 x + 7 |$

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

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

Good luck!