Step-by-Step Solution

Step-by-Step Solution

Step 1: Use the Absolute Value Zero Property

By definition of the absolute value function:

Therefore:

Step 2: Factor the Quadratic Trinomial

Find two numbers whose product is $4$ and whose sum is $5$. These numbers are $1$ and $4$:

Step 3: Solve for the Real Roots

Using the zero-product property:

Step 4: Graphical Interpretation

The curve $y = |x^2 + 5x + 4|$ touches the horizontal line $y = 0$ (the $x$-axis) at two sharp vertices (cusps) located at $x = -4$ and $x = -1$.