ANSWER
See attachment.
EXPLANATION
The given function is
[tex]y = {x}^{2} + 4x + 5[/tex]
When we compare this function to
[tex]y = a{x}^{2} + bx + c[/tex]
We have a=1, b=4 and c=5
We put this inside the formula for the discriminant, which is
[tex]D = {b}^{2} - 4ac[/tex]
[tex]D = {4}^{2} - 4(1)(5)[/tex]
[tex]D = 16 - 20 = - 4[/tex]
Since the discriminant is negative, the function has no x-intercepts.
The graph of this function is the one hanging in the air above the x-axis and opens upwards.
