Question

the graph below can be used to solve which equation?
$|x + 2| - 5 = (x - 1)(x - 3)$
$|x + 2| - 5 = -(x - 1)(x - 3)$
$|x - 2| - 5 = -(x - 1)(x - 3)$
$|x - 2| - 5 = -(x + 1)(x + 3)$

Explanation:

Step1: Identify absolute value graph

The red V-shaped graph has its vertex at $(-2, -5)$. The vertex form of an absolute value function is $y=|x-h|+k$, where $(h,k)$ is the vertex. Substituting $h=-2$, $k=-5$, we get:
$y = |x + 2| - 5$

Step2: Identify quadratic graph

The blue parabola opens downward, has x-intercepts at $x=1$ and $x=3$. The factored form of a quadratic is $y=a(x-r_1)(x-r_2)$. For downward opening, $a=-1$, $r_1=1$, $r_2=3$:
$y = -(x - 1)(x - 3)$

Step3: Set functions equal

To find the equation solved by their intersection, set the two functions equal:
$|x + 2| - 5 = -(x - 1)(x - 3)$

Answer:

B. $|x + 2| - 5 = -(x - 1)(x - 3)$