The function y = c(x - 3) is a straight line, and the function y = x^2 - 2x + 6 is a parabola. You're needing to find values of c so that the straight line passes the parabola off to one side.

To find where the lines donotintersect, we find first where theydointersect; the solution will be theothervalues of c.

Applyingthe Quadratic Formula, we get:

So there will be valid solutions (and thus intersections) for (c + 2)(c - 10)>0. To find the solution, you need tosolve the quadratic inequality.

The zeroes of (c + 2)(c - 10) are obviously at c = -2 and c = 10. The parabola corresponding to y = (c + 2)(c - 10) will open upward, so the quadratic will be positive (that is, the parabola will be above the x-axis) on the ends, before the first zero and after the second zero.

So which intervals give intersections? Then which interval does not?