Find the Coordinates of the Intersection Points of a Parabola and a Line: y = x ^ 2 + 4x-4 and y = 2x + 11

If the graphs intersect, then their ordinates y are equal, therefore:

x² + 4 * x – 4 = 2 * x + 11,

x² + 2 * x – 15 = 0.

By Vieta’s theorem, we have the roots (abscissas of the intersection points of the graphs):

x1 = -5 and x2 = 3.

Therefore, the ordinates of the intersection points are:

y1 = 2 * x1 + 11 = 1,

y2 = 2 * x2 + 11 = 17.

Answer: the graphs intersect at two points (-5; 1) and (3; 17).