find a formula for the quad. function whose graph has vertex @ (5,4) and its y-int at y=-4

We have that

y = a (x - 5)^2 + 4

And if the y intercept is - 4, then (0, -4) is on the graph, we have

- 4 = a(0 - 5)^2 + 4

- 4 = 25a + 4     subtract 4 from both sides

-8 = 25a      divide both sides by 25

a = -8/25

So......the function is

y = (-8/25) ( x - 5)^2 + 4     simplify

y = (-8/25) ( x ^2 - 10x + 25) + 4

y = (-8/25)x^2 + (16/5)x - 8 + 4

y = (-25/8)x^2 + (16/5)x - 4