tmua 2019 Q20

tmua · Uk · paper1 1 marks Curve Sketching Number of Solutions / Roots via Curve Analysis
What is the complete range of values of $k$ for which the curves with equations
$$y = x^3 - 12x$$
and
$$y = k - (x-2)^2$$
intersect at three distinct points, of which exactly two have positive $x$-coordinates?
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What is the complete range of values of $k$ for which the curves with equations

$$y = x^3 - 12x$$

and

$$y = k - (x-2)^2$$

intersect at three distinct points, of which exactly two have positive $x$-coordinates?