Question

Write the equation of the polynomial (of lowest possible degree) which needs the given conditions. Write the equation in factored for.

Has a local minimum at the point (-2,0) and a triple zero at x=3

Answer 1

given: 3 zeros ( x-intercept when y=0)
use the equation \[\rm f(x)=a(x-z_1)(x-z_2)(x-z_3)\] to find polynomial where (x-z) are the factors.
x=3 subtract 3 from both side to write it as a factor we will get `x-3=0`
since there are triple zeros at x=3 the equation will be
\[\rm f(x)=a(x-3)(x-3)(x-3)\]
f(x) is same as y
plugin the given points to solve for a