Question

Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms.

Answer 1

Answer:

g(x) = (11/12)x³ +(11/2)x² +(55/12)x -11

Step-by-step explanation:

A polynomial with zero "a" will have (x -a) as a factor. Your 3rd-degree polynomial will have the three factors ...

... f(x) = (x -(-4))·(x -(-3))·(x -1)

This will have a y-intercept of (4·3·(-1)) = -12. In order to move it to -11, we need to vertically scale this function by a factor of 11/12. Then our poynomial is ...

... g(x) = (11/12)(x+4)(x+3)(x-1)

Multiplying this out, you get ...

... g(x) = (11/12)x³ +(11/2)x² +(55/12)x -11