find a formula for the quad function whose graph has y-int @ y=7 and zeros at x=1 and x=5

We have that

y  = a( x - 1) ( x - 5)

And if the y intercept is 7.....then the point (0, 7) is on the graph.....so we have

7 = a(0 - 1) (0 - 5)   

7 = a (5)     divide both sides by 35

a = 7/5 

So....the function is

y = (7/5)(x - 1) ( x - 5)

y = (7/5) (x^2 -6x + 5)

y = (7/5)x^2 - (42/5)x + 7