Question

riting a polynomial function of a graph
use the fact that the graph passes through (0, 36) to find the coefficient a in
f(x) = a(x + 3)(x + 1)(x - 2)(x - 3).

a =
the graph is a polynomial function graph with a point (0,36) marked, and the x-intercepts are at -3, -1, 2, 3 (from the roots of the polynomial). the graph has arrows indicating end behavior, and a grid with x from -4 to 4 and y from -40 to 40.

Explanation:

Step1: Substitute x=0, y=36

Substitute \( x = 0 \) and \( f(0) = 36 \) into \( f(x)=a(x + 3)(x + 1)(x - 2)(x - 3) \).
\( 36=a(0 + 3)(0 + 1)(0 - 2)(0 - 3) \)

Step2: Simplify the right side

Calculate the product: \( (3)(1)(-2)(-3)=3\times1\times6 = 18 \).
So, \( 36 = 18a \).

Step3: Solve for a

Divide both sides by 18: \( a=\frac{36}{18}=2 \).

Answer:

2