Find the coordinates of A, the x-intercepts of the parabola, and the other intersection point C of the parabola y = x2 − 6x + 8 and the line y = 3x − 6.

Point A is an intersection of the parabola and the line. To find the intersection points, set the $y$-values equal.

X-intercepts occur when $y = 0$.

Point C is the other intersection of the parabola and the line. From part a), the $x$-coordinates of the intersection points are $x = 2$ and $x = 7$. Since A has $x=2$, C must have $x=7$.

The average rate of change between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by $\frac{y_2 - y_1}{x_2 - x_1}$.