Find a formula for quadratic function whose graph has its vertex at (1,4) and its y-intercept at y=-6

We have  the form

y = ax^2  + bx  +  c

If  the y intercept is  -6,   then  c   = -6

The x coordinate  of the vertexx is given by  -b/[2a]   = 1  which  implies  that  - b  = 2a  ⇒ b = -2a

And     we  know that

4  = a^(1)^2  - 2a (1)  - 6    simplify

4 = a - 2a  - 6     add 6 to both sides

10  =  -a      ⇒   a   =  -10    and b  (-2)(-10)   = 20

So....the  function  is

y = -10x^2  + 20x  - 6