To determine the nature of the graph using the end behaviour, we have to find out y-value using two values of x, one in the negative side and one in the positive side.
[tex]\begin{gathered} y=\text{ x}^2\text{ - 2x } \\ Let^{\prime}s\text{ use -2 and 2 values and replace it in the equation} \\ y=\text{ \lparen-2\rparen}^2\text{ - 2 \lparen-2\rparen} \\ y=\text{ 4 + 4} \\ y=\text{ 8} \\ \\ y=\text{ \lparen2\rparen}^2\text{ - 2\lparen2\rparen} \\ y=\text{ 4 - 4} \\ y=\text{ 0 } \end{gathered}[/tex]Therefore, when x-value is negative(left side) it tends to go up and when x-value is positive (right side), it tends to go down.
The answer is: up on left and down on right.