Find the vertex by completing the square to convert the quadratic to the form of y=(x-a)^2+K
In this case y= (x+4)^2-1
X intercepts should be found by factorizing. (x+3)(x+5) are the factors in this case. So x=-3 or x=-5 This means when y=0 x=-3 or x=-5. The smaller x value coordinate will then be (-5,0) and the larger will be (-3,0).
Then to find the y intercept simply plug in 0 for your x value in your original equation. When you solve this you should get y=15 when x=0. So the coordinates would be (0,15)
Let me know if you are still confused! Hope that helps.