Considering the graphs of y = 3x + c and y^2 = 6x, where c is a real constant, determine all values of c for which the graphs intersect in two distinct points.
I'm not entirely sure of where to start so any help is greatly appreciated.
Considering the graphs of y = 3x + c and y^2 = 6x, where c is a real constant, determine all values of c for which the graphs intersect in two distinct points.
I'm not entirely sure of where to start so any help is greatly appreciated.
Hello, Naples!
First, find the intersections . . .Considering the graphs of: . .where is a real constant,
determine all values of c for which the graphs intersect in two distinct points.
The first equation gives us: .
Substitute into the second: .
Quadratic Formula: .
The quadratic has two roots if the discriminant is positive: .
Therefore: .