SOLUTION: How would you find the equation for the quadratic function that has zeros 5 and 1 and f(0)=1?

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: How would you find the equation for the quadratic function that has zeros 5 and 1 and f(0)=1?      Log On


   

Question 403687: How would you find the equation for the quadratic function that has zeros 5 and 1 and f(0)=1?
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Let f%28x%29+=+ax%5E2+%2B+bx+%2B+c
==> f%28x%29+=+a%28x%5E2+%2B+%28bx%29%2Fa++%2Bc%2Fa+%29
Then from the given roots, b/a = -6, and c/a = 5, from the product and sum of roots formulas for the quadratic equation. Also, c = 1, from f(0) = 1.
Then 1 = 5a, or a = 1/5.
==> 5b = -6, or b = -6/5.