Given a quadratic function of the form f(x)= ax^2+ bx+ c, you can find the y- intercept simply by setting x= 0. No "quadratic formula" required there. To find the vertex, you want to rewrite the funtion as f(x)= (x- x_0)^2+ y_0 which you can do by "completing the square". Completing the square is a standard way of getting the "quadratic formula" but that formula is not needed. To find the x- intercept, you need to solve ax^2+ bx+ c= 0. You can use the quadratic formula to solve that but you could also factor or complete the square.