how do you solve f(x)= G(X)

and find the points of intersection of the graphs of the 2 functions

f(x)= x^2 + 5x+ 13
g(x)= 19

To solve the equation f(x) = g(x) and find the points of intersection of the two graphs, you need to set the two functions equal to each other and solve for x.

Step 1: Write the equation f(x) = g(x):
x^2 + 5x + 13 = 19

Step 2: Rearrange the equation to get a quadratic equation in standard form:
x^2 + 5x + 13 - 19 = 0
x^2 + 5x - 6 = 0

Step 3: Factor the quadratic equation:
(x + 6)(x - 1) = 0

Step 4: Set each factor equal to zero and solve for x:
x + 6 = 0 or x - 1 = 0

For x + 6 = 0:
x = -6

For x - 1 = 0:
x = 1

Step 5: The values x = -6 and x = 1 are the x-coordinates of the points of intersection of the two graphs.

To find the y-coordinates of these points, substitute the x-values we found into either f(x) or g(x) and evaluate:

For x = -6:
f(-6) = (-6)^2 + 5(-6) + 13 = 36 - 30 + 13 = 19

For x = 1:
f(1) = (1)^2 + 5(1) + 13 = 1 + 5 + 13 = 19

Therefore, the points of intersection of the graphs f(x) = x^2 + 5x + 13 and g(x) = 19 are (-6, 19) and (1, 19).