Set y=0 for the x intercepts, so expanding it we get x^2+4x+4+5=0 and x^2+4x+9 =0. Using the quadratic formula, we get that x= (-4+-sqrt(16-36))
right here, we see that the square root of something would be negative, so there are no x intercepts.
for the y intercepts, we set x=0 to get 2^2-5=-1.
for the vertex, we use x^2+4x+9 and -b/2a=the x value of the vertex =-4.
Plugging -4 into it, we get -16+16+9=9 for the y value of the vertex, getting (-4,9). Since -1 from (0, -1) is smaller than 9, the parabola forms a frowny face and goes downwards. Plug some random points in, and you'll have it down!