A graph having y intercept coincides with the Y axis. Similarly, a line having x interecept coincides with X axis. To find the x-intercept, put y=0 and solve the equation for x.
[tex]\begin{gathered} y=x^2+2x+5 \\ 0=x^2+2x+5 \end{gathered}[/tex]
Using determinant method, solve the above equation.
[tex]\begin{gathered} x=\frac{-2\pm\sqrt[]{2^2-4\times1+5}}{2\times1} \\ x=\frac{-2\pm\sqrt[]{-5}}{2} \end{gathered}[/tex]
So, we cannot obtain a solution for x. So, the graph has no x intercept.
To find the y-intercept, put x=0 and solve the equation for y.
[tex]\begin{gathered} y=x^2+2x+5 \\ y=0+0+5 \\ y=5 \end{gathered}[/tex]
Since the solution is y=5, the y intercept is 5.
Therefore, the given graph has a y intercept but not an X intercept
