Intersection of Quadratic Graphs

Consider the graphs of a quadratic function and a linear function on the same set of axes.
cutting
2 points of intersection
$b^2-4ac \gt 0$
Concave up
touching
1 point of intersection
$b^2-4ac = 0$
Concave up
missing
no points of intersection
$b^2-4ac \lt 0$
Concave up
In the graphs meet, the coordinates of the points of intersection of the graphs can be found by solving the two equations simultaneously.

Example 1

Find the coordinates of the points of intersection of the graphs with equations $y=x^2$ and $y=x+2$.

Example 2

Find the coordinates of the points of intersection of the graphs with equations $y=2x^2+2x-5$ and $y=x^2-2x$.

Example 3

$y=x^2-x-2$ and $y=x-k$ have two intersections. Find $k$.