Mathematico | Mathematico

The parabola

y = x^{2} - 4 x + 6

and the line

y = 2 x + 1

intersect at $P$ and $R .$

Find the angle $∠ P Q R,$ where $Q$ is the vertex of the parabola.

Find the coordinates of $P$ and $R$ by solving $x^{2} - 4 x + 6 = 2 x + 1.$

Complete the square on $y = x^{2} - 4 x + 6$ to find the vertex.

The formula for the distance between two points can find $P R, R Q$ and $Q P .$ Then the cosine rule applies.