Polynomial sketching

Question

Sketch a graph of a polynomial with a negative leading coefficient given zeroes -2 and 3 with multiplicity of 1 and 0 with multiplicity of 2.

Answer 1

So, here it says that there are 3 zeros (-2, 3, and 0)

With negative leading coefficient, we can start the polynomial with

f(x) = -(ax³+ bx²+cx+d)

With the zeros, we can say the f(x) in this form

f(x) = -a(x+2)b(x-3)c(x) where a, b, c are the multiplicity of each zeros

Thus, we know that the function is:

f(x) = -(x+2)(x-3)2x

Then graph it with calculator (or you can just sketch this)