how do i write an equation of a quadratic formula when given the roots and y intercept? is there a formula i can plug the numbers in or something?

9514 1404 393

  y = -3x^2 +3x +6

Step-by-step explanation:

For roots p and q, the equation can be written as ...

  y = a(x -p)(x -q)

The value of 'a' must be determined so that the product apq is equal to the y-intercept. One could say that the formula is ...

  y = (y-intercept)/(pq)·(x -p)(x -q)

For your given values of p = 2, q = -1, y-intercept = 6, this becomes ...

  y = 6/(2(-1))(x -2)(x +1)

  y = -3(x^2 -x -2) . . . . . simplifying a bit

  y = -3x^2 +3x +6