Question

what is the x-intercept of the graph of $y = -|x + 2|$?
a. $-2$
b. $-1$
c. $0$
d. $2$

Explanation:

Step1: Recall x-intercept definition

The x-intercept is the point where \( y = 0 \). So we set \( y = 0 \) in the equation \( y = -|x + 2| \).

$$ 0 = -|x + 2| $$

Step2: Solve for x

Multiply both sides by -1:

$$ |x + 2| = 0 $$

The absolute value of a number is 0 only when the number itself is 0. So:

$$ x + 2 = 0 $$

Subtract 2 from both sides:

$$ x = -2 $$

Answer:

A. -2