Answer:
Option (3)
Explanation:
From the graph attached,
Zeros of the function are, x = -3,
Graph of the polynomial touches x axis at x = -3, 1 and 3
Therefore, equation of the given function will be in the form of,
P(x) = [tex]k(x+3)^a(x-1)^b(x-3)^c[/tex]
Since, graph of the function just touches the x-axis, multiplicity of zero at x = -3 will be even and crosses x-axis so the multiplicity at x = 1 and 3 will be odd.
Therefore, possible function will be,
P(x) = [tex]k(x+3)^2(x-1)(x-3)[/tex]
Since, y-intercept of the function is at (0, -3),
P(0) = k(0 + 3)²(0 - 1)(0 - 3)
-3 = 27k
k = [tex]-\frac{3}{27}=-\frac{1}{9}[/tex]
Therefore, given polynomial function is,
P(x) = [tex]-\frac{1}{9}(x+3)^{2}(x-1)(x-3)[/tex]
Option (3) will be the correct option.
