



 
Hi Bianca, Let's think about this geometrically for the moment. $y = x^2  2x$ is a parabola and $y = k x  4$ is a line so you have three possible cases.
Now think algebraically. To determine where the parabola $y = x^2  2 x$ and the line $y = k x  4$ intersect substitute $y$ from the line equation into the equation of the parabola to obtain \[k x  4 = x^2  2 x.\] Simplify and set up the general quadratic expression to solve for $x,$ \[x = \frac{b \pm \sqrt{b^2  4 a c}}{2 a}.\] For your problem the important part of this expression is the discriminant, \[D = b^2  4 a c.\] If $D$ is negative Then the square root is imaginary and there is no solution (case 1). If $D$ is $0$ then there is exactly one solution (case 3) and if $D$ is positive there are two solution (case 2). Penny  


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