Someone me!

the vertex of the graph of a quadratic function is (3,1) and the y-intercept is (0,10). which of the following is the equation of the function?

a) y=2x^2-12x+10
b) y= -1/2x^2+3x-11/2
c) y=x^2-6x+10
d) y=2x^2-7x+4

The standard form of a parabole is: (y-k) = a(x-h)², Where (h , k) are the coordinates of the vertex
In the example Vertex (3,1) ,
so (y-1) = a(x-3)². (a)
Now let's calculate a. The y-intercept coordinates(0 , 10), Replace in (a) x by 0 & y by 10:
(10-1) = a(0 - 3)²
9 = 9a and a=1
The equation becomes : y-1 = (x-3)², Expand (y-1) = x²-6x+9
and finally y = x² - 6x +10 (ANSWER C)

The answer would be a