which equation choice could represent the graph shown below? answer f(x)=x(x - 6)(x - 6) f(x)=(x - 6)(x + 6)…

Explanation:

Step1: Identify the x - intercept

The graph touches the x - axis at x=-6. For a quadratic function in factored form (y = a(x - r_1)(x - r_2)), the x - intercepts are (x = r_1) and (x = r_2). Here, since the graph touches the x - axis at (x=-6), the factors should be of the form ((x + 6)) (because when (x=-6), (x+6 = 0)).

Step2: Determine the correct form

A quadratic function that touches the x - axis at a single point has a repeated root. The function should be of the form (f(x)=(x + 6)(x + 6)) which is a perfect - square quadratic.

Answer:

(f(x)=(x + 6)(x + 6))