Question

which of the following is the correct equation in factored form for the given graph?
y=(x + 3)(x + 1)
y=(-x + 3)(x + 1)
y=(-x - 3)(x - 1)
y=(-x - 3)(-x - 1)

Explanation:

Step1: Find x - intercepts from the graph

The x - intercepts of the graph are the points where the graph crosses the x - axis. If the x - intercepts are \(x = a\), \(x = b\), \(x = c\), then the factored form of the polynomial function is \(y=(x - a)(x - b)(x - c)\).

Step2: Identify x - intercepts values

From the graph, assume the x - intercepts are \(x=-3\), \(x = - 1\), \(x=1\). Then the factored form of the polynomial is \(y=(x + 3)(x + 1)(x - 1)\).

Answer:

The correct factored - form equation for the given graph is \(y=(x + 3)(x + 1)(x - 1)\) (the blue - colored option in the image if we assume the order of options from top to bottom).