Question

in the xy-plane, the line x + y=k, where k is a constant, is tangent to the graph of y=x^2+3x+1. What is the value of k?

Answer 1

slope of tangent line = dy/dx = 2x+3
k is y_intercept of tangent line

2x+3 = -1
x = -2
y = (-2)^2+3(-2)+1 = -1

tangent line passes through point (-2,-1)
k = x+y
k = -2 -1
k = -3

Answer 2

thank you! why did you set 2x+3= -1 though?
where did the -1 come from

Answer 3

oh sorry its the given slope of tangent line
x+y=k --> y = -x+k

Answer 4

OH! of course! haha thanks so much! i get it now

Answer 5

welcome