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

Question

Third-degree, with zeros of −5, −3, and 11, and a y-intercept of −15

Answer 1

Hello Kayla,

So your 3rd degree polynomial will have the format:

y = a*( x - zero₁)( x - zero₂)( x - zero₃).

You know the value of each zero so you can plug each zero where stated and you'd get:

y = a *(x+5)(x+3)(x-11). Let's call this equation E₁

You'll then use the y-intercept info to find the value of a.

By definition the y-intercept is the y-coordinate when x = 0, so you would replace every x by the number 0. You would also replace y by the y-intercept value.

If you do that, you will get an equation where the only unknown is a: -15 = a* (0+5)(0+3)(0-11)

From there, you solve for a, then you can plug that value into equation E₁

Cheers!