Question

How do you find the x and y intercepts for `y= -|x+10|`?

Answer 1

See a solution process below:

Explanation:

`y`-intercept:*

To find the `y`-intercept, set `x` equal to `0` and calculate `y`:

`y = -abs(x + 10)` becomes:

`y = -abs(0 + 10)`

`y = -abs(10)`

`y = -10`

The `y`-intercept is: `-10` or `(0, -10)`

`x`-intercept:*

To find the `x`-intercept, set `y` equal to `0` and solve for `x`:

`y = -abs(x + 10)` becomes:

`0 = -abs(x + 10)`

The absolute value function takes any negative or positive term and transforms it to its positive form. Therefore, we must solve the term within the absolute value function for both its negative and positive equivalent. However, because `-0` equals `0` we can just solve the term within the absolute value function once for `0`:

`0 = -(x + 10)`

`0 = -x - 10`

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

`x = 0 - 10`

`x = -10`

The `x`-intercept is: `-10` or `(-10, 0)`