In the picture the parabola passes through points $A=(1,3)$ and $B=(5,-5)$, and the line passes through points $C=(2,-2)$ and $D=(-2,-6)$.
Find the equation of the parabola.
As we can see, the scale of the graph is $2:1$ for $x$-axis and $1:1$ for $y$-axis.
I have found the equation of the parabola by looking at the graph and seeing that the point $(0,0)$ is in the parabola. Hence, we have $3$ points and we are done.
However, I have never used the points on the line. The exercise seems to want to use them in some way, so is there a method in which without "knowing" that the parabola passes through $(0,0)$ we can use the equation of the line?