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.

Using determinant method, solve the above equation.
![\begin{gathered} x=\frac{-2\pm\sqrt[]{2^2-4*1+5}}{2*1} \\ x=\frac{-2\pm\sqrt[]{-5}}{2} \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/ik5uvf37fzo5li4gm3hd26mcx7zmmwbysu.png)
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.

Since the solution is y=5, the y intercept is 5.
Therefore, the given graph has a y intercept but not an X intercept