377. Find the angles at which the parabola $y=x^{2}-x$ intersects the x-axis (Fig. 105).
Solution. Let's find the abscissas of the points of intersection of the parabola with the $O x$ axis, for which we solve the equation $x^{2}-x=0$, from which $x_{1}=0$ and $x_{2}=1$. The angle of the curve with the $O x$ axis is the angle that the tangent, drawn at the point of intersection of the curve with the $O x$ axis, forms with the positive direction of this axis. We will calculate the angular coefficients of the tangents to the parabola at the points $x_{1}=0$ and $x_{2}=1$. We find the derivative: $y^{\prime}=2 x-1$, from which $y^{\prime}(0)=-1$ and $y^{\prime}(1)=1$. Thus, $\operatorname{tg} \alpha_{1}=-1$ and $\operatorname{tg} \alpha_{2}=1$, i.e., $\alpha_{1}=$ $=3 \pi / 4$ and $\alpha_{2}=\pi / 4$.