A quadratic function is defined f(x) = 2x ^ 2 + 4x - 1 . A linear function is defined by g(x) = kx - 2 Algebraically determine a possible range of k so that the line f(x) INTERSECTS the curve g(x) .
if they intersect, then
2x^2+4x-1 = kx-2
2x^2 + (4-k)x + 1 = 0
the discriminant is (4-k)^2 - 8 = k^2-8k+8 = (k-4)^2 - 8
so if there are roots, that must not be negative, so
k <= 4-√8
or
k >= 4+√8
see the graphs at
www.wolframalpha.com/input?i=plot+y%3D2x%5E2%2B4x-1%2C+y%3D%284%2B%E2%88%9A8%29x-2%2C+y%3D%284-%E2%88%9A8%29x-2