Where does the curve defined by f(x) = x^2 + 2x-1 and the line y= 2x+3 intersect?

Given the function f(x) = x^2 + 2x
-1

and the line y= 2x+3

We
need to find the intersection points for the curve and the
line.

Then, we need to find the point that verifies f(x)
and y.

==> f(x) =
y

==> x^2 + 2x -1 = 2x
+3

We will subtract 2x from both
sides:

==> x^2 -1 =
3

Now we will add 1 to both
sides.

==> x^2 =
4

==> x = +-2

Then,
there are two points of intersection between the curve f(x) and the line
y.

==> f(2) = 4+4-1 =
7

==> f(-2) = 4-4-1 =
-1

Then, the points of intersection
are:

(-2, -1) and (2,7)