What is the quadratic function that is created with roots -3 and 1 and a vertex at (-1, -8)? and What is the quadratic function that is created with roots -10 and -6 and a vertex at (-8, -8)? THANKS! :)
the quadratic function that is created with roots -3 and 1 is: f(x) = a(x + 3)(x - 1) = a(x^2 + 2x - 3) = a(x^2 + 2x) - 3a . . . . . . . . (1) the quadratic function that is created with vertex at (-1, -8) is: a(x + 1)^2 - 8 = a(x^2 + 2x + 1) - 8 = a(x^2 + 2x) + a - 8 . . . . . . . . (2) From (1) and (2): a - 8 = -3a 4a = 8 a = 2 Therefore, required function is f(x) = 2(x^2 + 2x) - 3(2) = 2x^2 + 4x - 6
