How to find a polynomial with the given zeros of -1 and 4i

Step-by-step explanation:

We want to find the polynomial function whose zero are -1 and 4i.

Recall that non-real zeros come in pairs.

There if 4i is a zero, then the conjugate -4i is also a zero.

Therefore the factors of this polynomial are:

x+1, x+4i, and x-4i are factors of the given polynomial.

Let f(x) be the required polynomial, then we can write the polynomial in factored form as:

We expand the conjugate pair using difference of two squares to get:

Expand further using the distributive property to get:

horizontal translation of 2 units in the positive x direction

followed by

vertical translation of 3 units in the positive y direction