Question

Write a polynomial function with zeros at -5,1/2, 3 and a y intercept of 15.

Answer 1

For starters, write three factors which would give you the x-intercepts of -5, 1/2, and 3, those being (x+5), (x-1/2), and (x-3). Now, multiply the factors and set y equal to them, giving you $y=(x+5)(x-\frac{1}{2})(x-3)=x^3+1.5x^2-16x+7.5$. Now, find your y-intercept, $y=0^3+1.5(0)^2-16(0)+7.5=7.5$ and subtract it from your desired y-intercept, 15-7.5=7.5. Now add this to your equation, $y=(x^3+1.5x^2-16x+7.5)+7.5=x^3+1.5x^2-16x+15$ making your answer $y=x^3+1.5x^2-16x+15$.