write an equation for the polynomial graphed below. you can leave the function in factored form. *algebraic…

write an equation for the polynomial graphed below. you can leave the function in factored form. *algebraic work must be shown to retain points on quizzes, midterm or final question help: video post to forum submit question

write an equation for the polynomial graphed below. you can leave the function in factored form. *algebraic work must be shown to retain points on quizzes, midterm or final question help: video post to forum submit question

Answer

Explanation:

Step1: Identify the x - intercepts

The x - intercepts of the polynomial are (x=-3), (x = 1), and (x = 4). So the factors of the polynomial are ((x + 3)), ((x - 1)), and ((x - 4)). The polynomial can be written in the form (f(x)=a(x + 3)(x - 1)(x - 4)).

Step2: Find the value of (a)

We know that the polynomial passes through the point ((0,-2)). Substitute (x = 0) and (y=-2) into (f(x)=a(x + 3)(x - 1)(x - 4)): [ \begin{align*} -2&=a(0 + 3)(0 - 1)(0 - 4)\ -2&=a(3)(-1)(-4)\ -2&=12a\ a&=-\frac{1}{6} \end{align*} ]

Answer:

(f(x)=-\frac{1}{6}(x + 3)(x - 1)(x - 4))