Degree 5; roots of multiplicity 2 at x = 3 and x = 1, and a root of multiplicity 1 at x = −3; y-intercept at (0, 7).

Answer 1

Multiplicity means the degree the linear factor is raised to. Roots of even multiplicity, such as those at x = 1 and x = 3 here, will show up in the graph as tangent roots, meaning the graph will "bounce off" the x-axis, so the y-value will = 0 there, but the y-values do NOT change signs (this is important in calculus).

f(x) = 7/27·(x+3)(x-3)²(x-1)²

The 7/27 as the lead coefficient comes from plugging in x = 0 and noting that with a = 1, f(x) = 27