Question

which equation choice could represent the graph shown below? answer f(x) = (x + 7)(x - 4)(x + 5) f(x) = (x + 7)(x + 4)(x - 5) f(x) = (x + 7)(x - 4)(x - 5) f(x) = (x - 7)(x - 4)(x + 5)

Explanation:

Step1: Identify x - intercepts

From the graph, the curve crosses the x - axis at \( x=-7 \), \( x = 4 \), and \( x=5 \).

Step2: Write the factored form

If a polynomial has roots \( r_1\), \( r_2\), \( r_3\), then its factored form is \( f(x)=a(x - r_1)(x - r_2)(x - r_3) \) (assuming \( a = 1 \) for simplicity here). For roots \( x=-7\) (which is \( x-(-7)=x + 7\)), \( x = 4\) (which is \( x-4\)), and \( x = 5\) (which is \( x - 5\)), the polynomial is \( f(x)=(x + 7)(x - 4)(x - 5) \).

Answer:

\( f(x) = (x + 7)(x - 4)(x - 5) \)